## Lakshmikantham, Vangipuram

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 Author ID: lakshmikantham.vangipuram Published as: Lakshmikantham, V.; Lakshmikantham, Vangipuram External Links: MGP · GND
 Documents Indexed: 449 Publications since 1959, including 36 Books 12 Contributions as Editor Reviewing Activity: 253 Reviews Biographic References: 10 Publications Co-Authors: 112 Co-Authors with 388 Joint Publications 3,653 Co-Co-Authors
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### Serials

 49 Nonlinear Analysis. Theory, Methods & Applications 43 Journal of Mathematical Analysis and Applications 31 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 20 Applicable Analysis 20 Applied Mathematics and Computation 16 Nonlinear Studies 10 Journal of Mathematical and Physical Sciences 8 Nonlinear Analysis. Hybrid Systems 6 Communications in Applied Analysis 6 Proceedings of the Cambridge Philosophical Society 5 Computers & Mathematics with Applications 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Proceedings of the National Academy of Sciences, India. Section A 5 Stochastic Analysis and Applications 5 Dynamic Systems and Applications 5 Mathematics and its Applications (Dordrecht) 5 Mathematics in Science and Engineering 5 Pure and Applied Mathematics, Marcel Dekker 4 Archive for Rational Mechanics and Analysis 4 Annales Polonici Mathematici 4 Journal of Computational and Applied Mathematics 4 Journal of Optimization Theory and Applications 4 Journal of Integral Equations 4 Journal of Applied Mathematics and Stochastic Analysis 4 Neural, Parallel & Scientific Computations 4 Nonlinear Dynamics and Systems Theory 3 Michigan Mathematical Journal 3 Proceedings of the American Mathematical Society 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 Differential and Integral Equations 3 Nonlinear World 3 Mathematical Problems in Engineering 3 Mathematical Inequalities & Applications 3 Nonlinear Analysis. Real World Applications 3 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 2 Revue Roumaine de Mathématiques Pures et Appliquées 2 Rocky Mountain Journal of Mathematics 2 Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle Série 2 Mathematical Systems Theory 2 Transactions of the American Mathematical Society 2 SIAM Journal on Mathematical Analysis 2 Journal of Difference Equations and Applications 2 Discrete and Continuous Dynamical Systems 2 Journal of Applied Analysis 2 Journal of Inequalities and Applications 2 Lecture Notes in Pure and Applied Mathematics 2 Atlantis Studies in Mathematics for Engineering and Science 2 Boletim da Sociedade de Matemática de São Paulo 1 Avtomatika i Telemekhanika 1 Analele Științifice ale Universității Al. I. Cuza din Iași. (Serie Nouă.) Secțiunea Ia. Matematică-Informatică 1 Analele Universității din Timișoara. Științe Matematice 1 Bulletin of the Calcutta Mathematical Society 1 Bulletin of the London Mathematical Society 1 Conferenze del Seminario di Matematica dell’Università di Bari 1 Control and Cybernetics 1 Fuzzy Sets and Systems 1 IEEE Transactions on Automatic Control 1 Journal of Differential Equations 1 The Journal of the Indian Mathematical Society. New Series 1 Journal of the Korean Mathematical Society 1 Mathematics and Computers in Simulation 1 The Mathematics Student 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Tohoku Mathematical Journal. Second Series 1 Yokohama Mathematical Journal 1 Zeitschrift für Analysis und ihre Anwendungen 1 Gaṇita-Bhāratī 1 Journal of Applied Mathematics and Simulation 1 Applied Mathematics Letters 1 Panamerican Mathematical Journal 1 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 1 Prikladnaya Mekhanika 1 SIAM Journal on Applied Mathematics 1 Systems Analysis, Modelling Simulation 1 Analele Științifice ale Universității Al. I. Cuza din Iași. Serie Nouă. Matematică 1 Facta Universitatis. Series Mechanics, Automatic Control and Robotics 1 International Applied Mechanics 1 Nonlinear Times and Digest 1 Memoirs on Differential Equations and Mathematical Physics 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Differential Equations and Dynamical Systems 1 Neliniĭni Kolyvannya 1 Nonlinear Functional Analysis and Applications 1 Archives of Inequalities and Applications 1 Bollettino della Unione Matematica Italiana. Series IV 1 Bollettino della Unione Matematica Italiana. Series V. A 1 Buletinul Institutului Politehnic din Iași, New Series 1 North-Holland Mathematics Studies 1 Series in Real Analysis 1 Statistics: Textbooks and Monographs 1 Systems & Control: Foundations & Applications 1 Stability and Control: Theory, Methods, and Applications 1 European Journal of Pure and Applied Mathematics 1 Anais da Academia Brasileira de Ciências 1 Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics
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### Fields

 302 Ordinary differential equations (34-XX) 54 Partial differential equations (35-XX) 45 Operator theory (47-XX) 34 Integral equations (45-XX) 26 Systems theory; control (93-XX) 23 Numerical analysis (65-XX) 18 General and overarching topics; collections (00-XX) 18 Real functions (26-XX) 13 Difference and functional equations (39-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 13 Probability theory and stochastic processes (60-XX) 10 History and biography (01-XX) 10 Dynamical systems and ergodic theory (37-XX) 7 Functional analysis (46-XX) 6 Biology and other natural sciences (92-XX) 5 General topology (54-XX) 4 Mathematical logic and foundations (03-XX) 4 Fluid mechanics (76-XX) 4 Operations research, mathematical programming (90-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 1 Measure and integration (28-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

385 Publications have been cited 14,606 times in 9,798 Documents Cited by Year
Theory of impulsive differential equations. Zbl 0719.34002
Lakshmikantham, V.; Bajnov, D. D.; Simeonov, P. S.
1989
Nonlinear problems in abstract cones. Zbl 0661.47045
Guo, Dajun; Lakshmikantham, V.
1988
Theory of fractional dynamic systems. Zbl 1188.37002
Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J.
2009
Differential and integral inequalities. Theory and applications. Vol. I: Ordinary differential equations. Zbl 0177.12403
Lakshmikantham, V.; Leela, S.
1969
Fixed point theorems in partially ordered metric spaces and applications. Zbl 1106.47047
2006
Basic theory of fractional differential equations. Zbl 1161.34001
Lakshmikantham, V.; Vatsala, A. S.
2008
Monotone iterative techniques for nonlinear differential equations. Zbl 0658.35003
Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S.
1985
Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Zbl 1176.54032
Lakshmikantham, V.; Ćirić, Ljubomir
2009
Dynamic systems on measure chains. Zbl 0869.34039
Lakshmikantham, V.; Sivasundaram, S.; Kaymakcalan, B.
1996
Theory of fractional functional differential equations. Zbl 1162.34344
Lakshmikantham, V.
2008
Coupled fixed points of nonlinear operators with applications. Zbl 0635.47045
Guo, Dajun; Lakshmikantham, V.
1987
Stability analysis of nonlinear systems. Zbl 0676.34003
Lakshmikantham, V.; Leela, S.; Martynyuk, A. A.
1989
On the concept of solution for fractional differential equations with uncertainty. Zbl 1188.34005
Agarwal, Ravi P.; Lakshmikantham, V.; Nieto, Juan J.
2010
Theory of difference equations: Numerical methods and applications. Zbl 0683.39001
Lakshmikantham, V.; Trigiante, D.
1988
Nonlinear differential equations in abstract spaces. Zbl 0456.34002
Lakshmikantham, V.; Leela, S.
1981
Monotone iterative techniques for discontinuous nonlinear differential equations. Zbl 0804.34001
Heikkilä, Seppo; Lakshmikantham, V.
1994
An introduction to nonlinear boundary value problems. Zbl 0286.34018
Bernfeld, Stephen R.; Lakshmikantham, V.
1974
Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. Zbl 0694.34001
Byszewski, Ludwik; Lakshmikantham, V.
1991
Oscillation theory of differential equations with deviating arguments. Zbl 0832.34071
Ladde, G. S.; Lakshmikantham, V.; Zhang, B. G.
1987
Nonlinear integral equations in abstract spaces. Zbl 0866.45004
Guo, Dajun; Lakshmikantham, V.; Liu, Xinzhi
1996
Theory of fuzzy differential equations and inclusions. Zbl 1072.34001
Lakshmikantham, V.; Mohapatra, Ram N.
2003
General uniqueness and monotone iterative technique for fractional differential equations. Zbl 1161.34031
Lakshmikantham, V.; Vatsala, A. S.
2008
Oscillation theory of differential equations with deviating arguments. Zbl 0622.34071
Ladde, G. S.; Lakshmikantham, V.; Zhang, B. G.
1987
Theory of set differential equations in metric spaces. Zbl 1156.34003
Lakshmikantham, V.; Gnana Bhaskar, T.; Vasundhara Devi, J.
2006
Generalized quasilinearization for nonlinear problems. Zbl 0997.34501
Lakshmikantham, V.; Vatsala, A. S.
1998
Theory of fractional differential inequalities and applications. Zbl 1159.34006
Lakshmikantham, V.; Vatsala, A. S.
2007
Random differential inequalities. Zbl 0466.60002
1980
Vector Lyapunov functions and stability analysis of nonlinear systems. Zbl 0721.34054
Lakshmikantham, V.; Matrosov, V. M.; Sivasundaram, S.
1991
Differential equation s in abstract spaces. Zbl 0257.34002
1972
Practical stability of nonlinear systems. Zbl 0753.34037
Lakshmikantham, V.; Leela, S.; Martynyuk, A. A.
1990
Uniqueness and nonuniqueness criteria for ordinary differential equations. Zbl 0785.34003
Agarwal, R. P.; Lakshmikantham, V.
1993
Theory of integro-differential equations. Zbl 0849.45004
Lakshmikantham, V.; Rao, M. Rama Mohana
1995
Equations with unbounded delay: A survey. Zbl 0449.34048
Corduneanu, C.; Lakshmikantham, V.
1980
Stability analysis in terms of two measures. Zbl 0797.34056
Lakshmikantham, V.; Liu, X. Z.
1993
Basic results on hybrid differential equations. Zbl 1206.34020
Dhage, Bapurao C.; Lakshmikantham, V.
2010
Theory of fractional differential equations in a Banach space. Zbl 1146.34042
Lakshmikantham, V.; Vasundhara Devi, J.
2008
Existence and monotone method for periodic solutions of first-order differential equations. Zbl 0525.34031
Lakshmikantham, V.; Leela, S.
1983
Trends in the theory of impulsive differential equations. Zbl 0718.34011
Lakshmikantham, V.
1989
Oscillations of higher-order retarded differential equations generated by the retarded argument. Zbl 0273.34052
1972
Nagumo-type uniqueness result for fractional differential equations. Zbl 1177.34003
Lakshmikantham, V.; Leela, S.
2009
Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces. Zbl 1176.54030
Ćirić, Ljubomir; Lakshmikantham, V.
2009
Theory of difference equations: numerical methods and applications. 2nd ed. Zbl 1014.39001
Lakshmikantham, V.; Trigiante, Donato
2002
Theory of differential equations with unbounded delay. Zbl 0823.34069
Lakshmikantham, V.; Wen, Lizhi; Zhang, Binggen
1994
A Krasnoselskii-Krein-type uniqueness result for fractional differential equations. Zbl 1177.34004
Lakshmikantham, V.; Leela, S.
2009
Monotone iterative technique for differential equations in a Banach space. Zbl 0523.34057
Du, S. W.; Lakshmikantham, V.
1982
Remarks on first and second order periodic boundary value problems. Zbl 0532.34029
Lakshmikantham, V.; Leela, S.
1984
Existence and interrelation between set and fuzzy differential equations. Zbl 1035.34064
Lakshmikantham, V.; Tolstonogov, A. A.
2003
Revisiting fuzzy differential equations. Zbl 1095.34511
Bhaskar, T. Gnana; Lakshmikantham, V.; Devi, Vasundhara
2004
Initial and boundary value problems for fuzzy differential equations. Zbl 1048.34015
O’Regan, Donal; Lakshmikantham, V.; Nieto, Juan J.
2003
Multiple solutions of two-point boundary value problems of ordinary differential equations in Banach spaces. Zbl 0645.34014
Guo, Dajun; Lakshmikantham, V.
1988
Stability criteria for impulsive differential equations in terms of two measures. Zbl 0688.34031
Lakshmikantham, V.; Liu, Xinzhi
1989
Periodic boundary value problems of first and second order differential equations. Zbl 0712.34058
Lakshmikantham, V.
1989
Extremal solutions, comparison principle and stability criteria for impulsive differential equations with variable times. Zbl 0807.34064
Kaul, S.; Lakshmikantham, V.; Leela, S.
1994
On the existence of weak solutions of differential equations in nonreflexive Banach spaces. Zbl 0379.34041
Cramer, Evin; Lakshmikantham, V.; Mitchell, A. R.
1978
On quasi stability for impulse differential systems. Zbl 0688.34032
Lakshmikantham, V.; Liu, Xinzhi
1989
Hybrid systems on time scales. Zbl 1032.34050
Lakshmikantham, V.; Vatsala, A. S.
2002
Method of variation of parameters for dynamic systems. Zbl 0920.34001
Lakshmikantham, V.; Deo, S. G.
1998
Set valued functions in Fréchet spaces: continuity, Hukuhara differentiability and applications to set differential equations. Zbl 1190.49025
Galanis, G. N.; Bhaskar, T. Gnana; Lakshmikantham, V.; Palamides, P. K.
2005
Lyapunov theory for fractional differential equations. Zbl 1191.34007
Lakshmikantham, V.; Leela, S.; Sambandham, M.
2008
Comparison principle for impulsive differential equations with variable times and stability theory. Zbl 0797.34058
Lakshmikantham, V.; Leela, S.; Kaul, S.
1994
Nonsmooth analysis and fractional differential equations. Zbl 1237.49022
Vasundhara Devi, J.; Lakshmikantham, V.
2009
Cone-valued Lyapunov functions. Zbl 0357.34051
Lakshmikantham, V.; Leela, S.
1977
Periodic boundary value problems for second order impulsive differential systems. Zbl 0712.34033
Hu, Shouchuan; Lakshmikantham, V.
1989
Periodic boundary value problems for systems of first order impulsive differential equations. Zbl 0732.34040
Bajnov, D. D.; Khristova, S. G.; Hu, Shouchuan; Lakshmikantham, V.
1989
Fixed point theorems of operators with PPF dependence in Banach spaces. Zbl 0375.47027
Bernfeld, Stephen R.; Lakshmikantham, V.; Reddy, Y. M.
1977
A stacking theorem approach for fuzzy differential equations. Zbl 1042.34027
Agarwal, Ravi P.; O’Regan, Donal; Lakshmikantham, V.
2003
Set differential equations and flow invariance. Zbl 1047.34010
2003
Further improvement of generalized quasilinearization method. Zbl 0855.34012
Lakshmikantham, V.
1996
On perturbing Lyapunov functions. Zbl 0354.34050
Lakshmikantham, V.; Leela, S.
1976
Nonlinear variation of parameters formula for set differential equations in a metric space. Zbl 1153.34313
Bhaskar, T. Gnana; Lakshmikantham, V.; Vasundhara Devi, J.
2005
Viability theory and fuzzy differential equations. Zbl 1074.34009
Agarwal, Ravi P.; O’Regan, Donal; Lakshmikantham, V.
2005
An extension of the method of quasilinearization. Zbl 0806.34013
Lakshmikantham, V.
1994
Improved generalized quasilinearization (GQL) method. Zbl 0830.65068
Lakshmikantham, V.; Leela, S.; McRae, Farzana A.
1995
Methods of generalized quasilinearization for periodic boundary value problems. Zbl 0855.34011
Lakshmikantham, V.; Shahzad, N.; Nieto, Juan J.
1996
Theory of causal differential equations. Zbl 1219.34002
Lakshmikantham, V.; Leela, S.; Drici, Zahia; McRae, F. A.
2009
Global existence and asymptotic equilibrium in Banach spaces. Zbl 0273.34040
1972
Impulsive hybrid systems and stability theory. Zbl 0901.34018
Lakshmikantham, V.; Liu, X.
1998
Fractional differential equations with a Krasnoselskii-Krein type condition. Zbl 1181.34008
Bhaskar, T. Gnana; Lakshmikantham, V.; Leela, S.
2009
Stability of motion: the comparison method. Stability: theory, methods and applications. (Устойчивость движения: метод сравнения. Устойчивость: теория, методы и приложения.) Zbl 0852.34057
Lakshmikantham, V.; Leela, S.; Martynyuk, A. A.
1991
Positive solutions of nonlinear integral equations arising in infectious diseases. Zbl 0658.45012
Guo, Dajun; Lakshmikantham, V.
1988
The method of upper, lower solutions and hyperbolic partial differential equations. Zbl 0569.35056
Lakshmikantham, V.; Pandit, S. G.
1985
Singular $$(p,n-p)$$ focal and $$(n,p)$$ higher order boundary value problems. Zbl 0977.34017
Agarwal, Ravi P.; O’Regan, Donal; Lakshmikantham, V.
2000
Comparison principle and nonlinear contractions in abstract spaces. Zbl 0296.47037
Eisenfeld, J.; Lakshmikantham, V.
1975
Differential equations in metric spaces: An introduction and an application to fuzzy differential equations. Zbl 1057.34061
Lakshmikantham, V.; Nieto, Juan J.
2003
Existence of solutions of boundary value problems for nonlinear second order systems in a Banach space. Zbl 0385.34035
Chandra, Jahdish; Lakshmikantham, V.; Mitchell, A. R.
1978
Monotone iterative technique for functional differential equations with retardation and anticipation. Zbl 1121.34065
Bhaskar, T. Gnana; Lakshmikantham, V.; Vasundhara Devi, J.
2007
Existence of positive solutions for singular initial and boundary value problems via the classical upper and lower solution approach. Zbl 1010.34011
Agarwal, R. P.; O’Regan, Donal; Lakshmikantham, V.; Leela, S.
2002
Monotone flows and rapid convergence for nonlinear partial differential equations. Zbl 1017.35001
Lakshmikantham, V.; Köksal, S.
2003
Two-point boundary value problems associated with nonlinear fuzzy differential equations. Zbl 1022.34051
Lakshmikantham, V.; Murty, K. N.; Turner, J.
2001
Generalized quasilinearization. Zbl 0799.34012
Lakshmikantham, V.; Malek, S.
1994
Further generalization of generalized quasilinearization method. Zbl 0817.34005
1994
Extensions of the method of quasilinearization. Zbl 0837.65068
Lakshmikantham, V.; Leela, S.; Sivasundaram, S.
1995
Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions. Zbl 1010.65041
Carl, S.; Lakshmikantham, V.
2002
Existence and uniqueness of solutions of delay differential equations on a closed subset of a Banach space. Zbl 0384.34040
Lakshmikantham, V.; Leela, S.; Moauro, V.
1978
A damped oscillator with piecewise constant time delay. Zbl 1016.34069
Wiener, Joseph; Lakshmikantham, V.
2000
Generalized quasilinearization for nonlinear first order ordinary differential equations. Zbl 0855.34013
Lakshmikantham, V.; Nieto, J. J.
1995
An upper and lower solution theory for singular Emden-Fowler equations. Zbl 1011.34013
Agarwal, R. P.; O’Regan, Donal; Lakshmikantham, V.; Leela, S.
2002
Differential equations with piecewise constant argument and impulsive equations. Zbl 0997.34076
Wiener, Joseph; Lakshmikantham, V.
2000
Stability theory for set differential equations. Zbl 1068.34047
Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J.
2004
Differential inequalities with initial time difference and applications. Zbl 0933.34007
Lakshmikantham, V.; Vatsala, A. S.
1999
Stability analysis of nonlinear systems. 2nd edition. Zbl 1405.93006
Lakshmikantham, Vangipuram; Leela, Srinivasa; Martynyuk, Anatoly A.
2015
On the concept of solution for fractional differential equations with uncertainty. Zbl 1188.34005
Agarwal, Ravi P.; Lakshmikantham, V.; Nieto, Juan J.
2010
Basic results on hybrid differential equations. Zbl 1206.34020
Dhage, Bapurao C.; Lakshmikantham, V.
2010
On global existence and attractivity results for nonlinear functional integral equations. Zbl 1197.45005
Dhage, Bapurao C.; Lakshmikantham, V.
2010
Theory of fractional dynamic systems. Zbl 1188.37002
Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J.
2009
Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Zbl 1176.54032
Lakshmikantham, V.; Ćirić, Ljubomir
2009
Nagumo-type uniqueness result for fractional differential equations. Zbl 1177.34003
Lakshmikantham, V.; Leela, S.
2009
Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces. Zbl 1176.54030
Ćirić, Ljubomir; Lakshmikantham, V.
2009
A Krasnoselskii-Krein-type uniqueness result for fractional differential equations. Zbl 1177.34004
Lakshmikantham, V.; Leela, S.
2009
Nonsmooth analysis and fractional differential equations. Zbl 1237.49022
Vasundhara Devi, J.; Lakshmikantham, V.
2009
Theory of causal differential equations. Zbl 1219.34002
Lakshmikantham, V.; Leela, S.; Drici, Zahia; McRae, F. A.
2009
Fractional differential equations with a Krasnoselskii-Krein type condition. Zbl 1181.34008
Bhaskar, T. Gnana; Lakshmikantham, V.; Leela, S.
2009
Fixed point theorems in ordered Banach spaces via quasilinearization. Zbl 1215.47045
Lakshmikantham, V.; Carl, S.; Heikkilä, S.
2009
The hybrid grand unified theory. Zbl 1188.81003
Lakshmikantham, V.; Escultura, E.; Leela, S.
2009
Revisiting the hybrid real number system. Zbl 1167.03311
Escultura, E.; Bhaskar, T. Gnana; Lakshmikantham, V.; Leela, S.
2009
Basic theory of fractional differential equations. Zbl 1161.34001
Lakshmikantham, V.; Vatsala, A. S.
2008
Theory of fractional functional differential equations. Zbl 1162.34344
Lakshmikantham, V.
2008
General uniqueness and monotone iterative technique for fractional differential equations. Zbl 1161.34031
Lakshmikantham, V.; Vatsala, A. S.
2008
Theory of fractional differential equations in a Banach space. Zbl 1146.34042
Lakshmikantham, V.; Vasundhara Devi, J.
2008
Lyapunov theory for fractional differential equations. Zbl 1191.34007
Lakshmikantham, V.; Leela, S.; Sambandham, M.
2008
Set differential equations in Fréchet spaces. Zbl 1147.58007
Galanis, George N.; Bhaskar, Tenali Gnana; Lakshmikantham, Vangipuram
2008
Stability theory for multi-order fractional differential equations. Zbl 1185.34007
Lakshmikantham, V.; Leela, S.
2008
Theory of fractional differential inequalities and applications. Zbl 1159.34006
Lakshmikantham, V.; Vatsala, A. S.
2007
Monotone iterative technique for functional differential equations with retardation and anticipation. Zbl 1121.34065
Bhaskar, T. Gnana; Lakshmikantham, V.; Vasundhara Devi, J.
2007
An existence theorem for set differential inclusions in a semilinear metric space. Zbl 1166.49019
de Blasi, F.; Lakshmikantham, V.; Bhaskar, T. Gnana
2007
Perspectives of fuzzy initial value problems. Zbl 1152.34041
Bede, Barnabás; Bhaskar, T. Gnana; Lakshmikantham, V.
2007
Functional differential systems with retardation and anticipation. Zbl 1138.34029
2007
The hybrid real number system. Zbl 1122.03312
Lakshmikantham, V.; Kovach, Danny
2007
The hybrid set theory. Zbl 1122.03309
Bhaskar, T. Gnana; Kovach, Danny; Lakshmikantham, V.
2007
Hybrid physics of the mind. Zbl 1197.00020
Lakshmikantham, V.
2007
Functional differential equations with anticipation. Zbl 1151.34325
Lakshmikantham, V.; Vasundhara Devi, J.
2007
Fixed point theorems in partially ordered metric spaces and applications. Zbl 1106.47047
2006
Theory of set differential equations in metric spaces. Zbl 1156.34003
Lakshmikantham, V.; Gnana Bhaskar, T.; Vasundhara Devi, J.
2006
Hybrid systems with time scales and impulses. Zbl 1109.34003
Lakshmikantham, V.; Vasundhara Devi, J.
2006
On initial-boundary value problems in bounded and unbounded domains for a class of nonlinear hyperbolic equations of the third order. Zbl 1106.35036
2006
Ancient and medieval astronomers and mathematicians of India. Zbl 1208.01001
Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J.
2006
Set valued functions in Fréchet spaces: continuity, Hukuhara differentiability and applications to set differential equations. Zbl 1190.49025
Galanis, G. N.; Bhaskar, T. Gnana; Lakshmikantham, V.; Palamides, P. K.
2005
Nonlinear variation of parameters formula for set differential equations in a metric space. Zbl 1153.34313
Bhaskar, T. Gnana; Lakshmikantham, V.; Vasundhara Devi, J.
2005
Viability theory and fuzzy differential equations. Zbl 1074.34009
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2005
Computational error and complexity in science and engineering. Zbl 1076.65045
Lakshmikantham, Vangipuram; Sen, Syamal K.
2005
Generalized quasilinearization versus Newton method. Zbl 1078.65037
Lakshmikantham, V.; Vatsala, A. S.
2005
The origin and history of mathematics. Zbl 1141.01003
Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J.
2005
Maximal solutions and existence theory for fuzzy differential and integral equations. Zbl 1106.47067
Agarwal, R. P.; O&rsquo;Regan, D.; Lakshmikantham, V.
2005
Nonresonant singular boundary value problems with sign changing nonlinearities. Zbl 1086.34020
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.; Leela, S.
2005
A note on upper and lower solutions for first order inclusions of upper semicontinuous or lower semicontinuous type. Zbl 1084.34010
Agarwal, R. P.; Frigon, M.; Lakshmikantham, V.; O&rsquo;Regan, D.
2005
Monotone approximations and rapid convergence. Zbl 1079.65066
Lakshmikantham, V.
2005
Revisiting fuzzy differential equations. Zbl 1095.34511
Bhaskar, T. Gnana; Lakshmikantham, V.; Devi, Vasundhara
2004
Stability theory for set differential equations. Zbl 1068.34047
Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J.
2004
Lyapunov stability for set differential equations. Zbl 1078.34032
2004
A generalized upper and lower solution method for singular initial value problems. Zbl 1098.34004
Agarwal, R. P.; O&rsquo;Regan, D.; Lakshmikantham, V.; Leela, S.
2004
Error in error-free computation for linear system. Zbl 1165.65328
Lakshmikantham, V.; Sen, S. K.; Mohanty, A.
2004
Fuzzy Volterra integral equations: a stacking theorem approach. Zbl 1069.45001
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2004
Formulas of Bendixson and Alekseev for difference equations. Zbl 1043.39007
Bohner, M.; Lakshmikantham, V.
2004
Lyapunov functions in metric spaces. Zbl 1089.34539
Lakshmikantham, V.; Vasundhara Devi, J.
2004
Theory of fuzzy differential equations and inclusions. Zbl 1072.34001
Lakshmikantham, V.; Mohapatra, Ram N.
2003
Existence and interrelation between set and fuzzy differential equations. Zbl 1035.34064
Lakshmikantham, V.; Tolstonogov, A. A.
2003
Initial and boundary value problems for fuzzy differential equations. Zbl 1048.34015
O&rsquo;Regan, Donal; Lakshmikantham, V.; Nieto, Juan J.
2003
A stacking theorem approach for fuzzy differential equations. Zbl 1042.34027
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2003
Set differential equations and flow invariance. Zbl 1047.34010
2003
Differential equations in metric spaces: An introduction and an application to fuzzy differential equations. Zbl 1057.34061
Lakshmikantham, V.; Nieto, Juan J.
2003
Monotone flows and rapid convergence for nonlinear partial differential equations. Zbl 1017.35001
Lakshmikantham, V.; Köksal, S.
2003
Set differential equations and monotone flows. Zbl 1090.34064
Lakshmikantham, V.; Vatsala, A. S.
2003
Discrete second order inclusions. Zbl 1047.39013
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2003
An upper and lower solution approach for nonlinear singular boundary value problems with $$y\prime$$ dependence. Zbl 1046.34033
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2003
Existence criteria for singular boundary value problems modelling the membrane response of a spherical cap. Zbl 1028.34016
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2003
Unified approach to monotone iterative technique for semilinear parabolic problems. Zbl 1024.35048
Köksal, S.; Lakshmikantham, V.
2003
Generalized proximal normals and flow invariance for differential inclusions. Zbl 1035.34009
2003
Generalized quasilinearization method for semilinear hyperbolic problems. Zbl 1026.35082
Gnana Bhaskar, T.; Köksal, S.; Lakshmikantham, V.
2003
Theory of difference equations: numerical methods and applications. 2nd ed. Zbl 1014.39001
Lakshmikantham, V.; Trigiante, Donato
2002
Hybrid systems on time scales. Zbl 1032.34050
Lakshmikantham, V.; Vatsala, A. S.
2002
Existence of positive solutions for singular initial and boundary value problems via the classical upper and lower solution approach. Zbl 1010.34011
Agarwal, R. P.; O&rsquo;Regan, Donal; Lakshmikantham, V.; Leela, S.
2002
Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions. Zbl 1010.65041
Carl, S.; Lakshmikantham, V.
2002
An upper and lower solution theory for singular Emden-Fowler equations. Zbl 1011.34013
Agarwal, R. P.; O&rsquo;Regan, Donal; Lakshmikantham, V.; Leela, S.
2002
Basic theory of fuzzy difference equations. Zbl 1023.39008
Lakshmikantham, V.; Vatsala, A. S.
2002
On the Dirichlet problem for fourth-order linear hyperbolic equations. Zbl 1004.35082
2002
Generalized quasilinearization and semilinear parabolic problems. Zbl 1011.35079
Carl, S.; Lakshmikantham, V.
2002
On the Dirichlet problem in a characteristic rectangle for higher order linear hyperbolic equations. Zbl 1004.35083
2002
On doubly periodic solutions of fourth-order linear hyperbolic equations. Zbl 1004.35080
2002
A unified monotone iterative technique for semilinear elliptic boundary value problems. Zbl 1140.35419
Köksal, S.; Lakshmikantham, V.
2002
Nonuniform nonresonance at the first eigenvalue for singular boundary value problems with sign changing nonlinearities. Zbl 1021.34016
Agarwal, R. P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2002
A new concept unifying Lyapunov and orbital stabilities. Zbl 1085.34532
Lakshmikantham, V.; Leela, S.
2002
A unified monotone iterative technique for nonlinear elliptic problems via nonvariational method. Zbl 1009.35036
Köksal, Semen; Lakshmikantham, V.
2002
Two-point boundary value problems associated with nonlinear fuzzy differential equations. Zbl 1022.34051
Lakshmikantham, V.; Murty, K. N.; Turner, J.
2001
Strict stability of differential equations. Zbl 1008.34041
Lakshmikantham, V.; Mohapatra, R. N.
2001
Strict practical stability of delay differential equation. Zbl 1035.34082
Lakshmikantham, V.; Zhang, Y.
2001
Basic results for fuzzy impulsive differential equations. Zbl 0993.34008
Lakshmikantham, V.; McRae, Farzana A.
2001
Fuzzy differential systems and the new concept of stability. Zbl 1007.34055
Lakshmikantham, V.; Leela, S.
2001
Strict practical stability of delay differential equation. Zbl 1037.34070
Lakshmikantham, V.; Zhang, Y.
2001
Basic properties of solutions of fuzzy differential equations. Zbl 0997.34051
Lakshmikantham, V.; Mohapatra, R. N.
2001
Generalized quasilinearization for quasilinear parabolic equations with nonlinearities of DC type. Zbl 0984.35087
Carl, S.; Lakshmikantham, V.
2001
Quadratic forms and nonlinear non-resonant singular second order boundary value problems of limit circle type. Zbl 0986.34014
Agarwal, R. P.; O&rsquo;Regan, D.; Lakshmikantham, V.
2001
Generalized quasilinearization and semilinear degenerate elliptic problems. Zbl 1172.35406
Lakshmikantham, V.; Leela, S.
2001
Existence criteria for singular initial value problems with sign changing nonlinearities. Zbl 1023.34001
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2001
Handbook of stochastic analysis and applications. Zbl 0979.00017
2001
Generalized quasilinearization and quasilinear elliptic problems. Zbl 1075.35523
Lakshmikantham, V.; Leela, S.
2001
An overview of integro-differential equations and variational Lyapunov method. Zbl 0983.45004
Stephens, Sonya A. F.; Lakshmikantham, V.
2001
Singular $$(p,n-p)$$ focal and $$(n,p)$$ higher order boundary value problems. Zbl 0977.34017
Agarwal, Ravi P.; O&rsquo;Regan, Donal; Lakshmikantham, V.
2000
A damped oscillator with piecewise constant time delay. Zbl 1016.34069
Wiener, Joseph; Lakshmikantham, V.
2000
Differential equations with piecewise constant argument and impulsive equations. Zbl 0997.34076
Wiener, Joseph; Lakshmikantham, V.
2000
Uncertain systems and fuzzy differential equations. Zbl 0966.34055
Lakshmikantham, V.
2000
...and 285 more Documents
all top 5

### Cited by 7,352 Authors

 228 Agarwal, Ravi P. 180 Lakshmikantham, Vangipuram 176 O’Regan, Donal 141 Nieto Roig, Juan Jose 114 Chen, Lansun 108 Liu, Lishan 100 Ntouyas, Sotiris K. 95 Benchohra, Mouffak 89 Wu, Yonghong 86 Ahmad, Bashir 78 Ge, Weigao 78 Liu, Xinzhi 78 Wang, Jinrong 70 Henderson, Johnny Lee 67 Băleanu, Dumitru I. 66 Shen, Jianhua 60 Cabada, Alberto 59 Li, Yongxiang 59 Sun, Ji Tao 58 Bainov, Drumi Dimitrov 58 Heikkilä, Seppo V. 54 Karapınar, Erdal 51 Jankowski, Tadeusz 51 Zhou, Yong 49 Feng, Meiqiang 49 Ladde, Gangaram S. 48 Leela, Srinivasa G. 48 Vatsala, Aghalaya S. 47 Shah, Kamal 46 Martynyuk, Anatoliĭ Andriĭovych 46 Tariboon, Jessada 45 Al-saedi, Ahmed Eid Salem 44 Jiao, Jianjun 43 Wang, Guotao 42 Graef, John R. 42 Stamova, Ivanka Milkova 41 Samet, Bessem 40 Khristova, Snezhana G. 40 Wang, Peiguang 39 Cui, Yujun 37 Džurina, Jozef 37 Zhang, Xuemei 36 Yan, Jurang 35 Aydi, Hassen Mohamed 35 Kumam, Poom 35 Li, Wan-Tong 35 Xu, Jiafa 34 Khan, Rahmat Ali 34 Ouahab, Abdelghani 34 Wong, Patricia J. Y. 34 Zhai, Chengbo 33 Choudhury, Binayak Samadder 33 Guo, Dajun 33 Meng, Xinzhu 33 Rodríguez-López, Rosana 33 Song, Xinyu 33 Sun, Jianping 33 Wei, Zhongli 32 Gumel, Abba B. 32 Jiang, Daqing 32 Li, Xiaodi 31 Chen, Haibo 31 Radenovic, Stojan 31 Teng, Zhi-dong 31 Zhang, Lihong 30 Abbas, Said 30 Abdeljawad, Thabet 30 Balachandran, Krishnan 29 Akhmet, Marat Ubaydulla 29 López Pouso, Rodrigo 29 Luca, Rodica 29 Luo, Zhiguo 29 Pandey, Dwijendra Narain 29 Shatanawi, Wasfi A. 29 Su, Hua 29 Xu, Daoyi 28 Sintunavarat, Wutiphol 28 Sivasundaram, Seenith 28 Slyn’ko, Vitalii Ivanovich 27 Carl, Siegfried 26 Chatzarakis, George E. 26 Erbe, Lynn Harry 26 He, Zhimin 26 Li, Yongkun 26 Stamov, Gani Trendafilov 26 Sun, Jingxian 25 Baculíková, Blanka 25 Cai, Shaohong 25 Cao, Jinde 25 Goodrich, Christopher S. 25 Li, Tongxing 25 Liu, Yansheng 25 Liu, Zhenhai 25 Ngo Van Hoa 25 Philos, Christos G. 25 Yan, Baoqiang 25 Zhang, Binggen 24 Ezzinbi, Khalil 24 Liu, Yuji 24 Sadarangani, Kishin B. ...and 7,252 more Authors
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### Cited in 536 Serials

 633 Journal of Mathematical Analysis and Applications 620 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 593 Applied Mathematics and Computation 526 Advances in Difference Equations 376 Computers & Mathematics with Applications 314 Abstract and Applied Analysis 300 Nonlinear Analysis. Theory, Methods & Applications 224 Boundary Value Problems 213 Fixed Point Theory and Applications 211 Applied Mathematics Letters 199 Journal of Computational and Applied Mathematics 164 Journal of Applied Mathematics and Computing 142 Applicable Analysis 142 Nonlinear Analysis. Real World Applications 139 Chaos, Solitons and Fractals 139 Mathematical and Computer Modelling 110 Discrete Dynamics in Nature and Society 104 Journal of Function Spaces 98 Journal of Inequalities and Applications 95 Communications in Nonlinear Science and Numerical Simulation 88 Journal of Differential Equations 88 Nonlinear Analysis. Hybrid Systems 78 Fuzzy Sets and Systems 69 Rocky Mountain Journal of Mathematics 68 Mediterranean Journal of Mathematics 68 Journal of Fixed Point Theory and Applications 62 Journal of Difference Equations and Applications 61 Automatica 61 Proceedings of the American Mathematical Society 60 Journal of the Franklin Institute 59 Stochastic Analysis and Applications 59 Mathematical Problems in Engineering 58 Nonlinear Dynamics 58 Fractional Calculus & Applied Analysis 58 Journal of Applied Mathematics 54 Journal of Nonlinear Science and Applications 49 Filomat 47 International Journal of Differential Equations 45 AIMS Mathematics 44 Differential Equations and Dynamical Systems 43 Mathematics and Computers in Simulation 43 Applied Mathematical Modelling 40 Ukrainian Mathematical Journal 38 Applied Mathematics and Mechanics. (English Edition) 37 Results in Mathematics 37 Nonlinear Analysis. Modelling and Control 36 Journal of Integral Equations and Applications 35 Czechoslovak Mathematical Journal 35 Journal of Optimization Theory and Applications 33 Mathematical Methods in the Applied Sciences 33 Computational and Applied Mathematics 33 Differential Equations 32 Acta Mathematicae Applicatae Sinica. English Series 31 International Journal of Control 31 International Journal of Systems Science 31 Systems & Control Letters 31 Journal of Mathematical Sciences (New York) 30 Information Sciences 30 Mathematica Slovaca 30 Positivity 29 Bulletin of the Australian Mathematical Society 27 Annali di Matematica Pura ed Applicata. Serie Quarta 27 Numerical Functional Analysis and Optimization 27 Discrete and Continuous Dynamical Systems. Series B 27 Fractional Differential Calculus 27 Journal of Mathematics 27 Open Mathematics 26 Transactions of the American Mathematical Society 26 Acta Applicandae Mathematicae 26 Acta Mathematica Sinica. English Series 26 International Journal of Biomathematics 25 Applied Mathematics. Series B (English Edition) 25 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 24 Mathematical Biosciences 24 International Journal of Computer Mathematics 24 Afrika Matematika 21 Zeitschrift für Analysis und ihre Anwendungen 21 Complexity 21 Advances in Mathematical Physics 19 Physics Letters. A 19 Rendiconti del Circolo Matemàtico di Palermo. Serie II 19 Tohoku Mathematical Journal. Second Series 19 Applications of Mathematics 19 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 19 Soft Computing 19 Asian-European Journal of Mathematics 18 Journal of Mathematical Biology 18 Demonstratio Mathematica 18 Acta Mathematica Hungarica 18 Thai Journal of Mathematics 18 Mathematical Sciences 18 International Journal of Applied and Computational Mathematics 17 Bulletin of Mathematical Biology 17 International Journal of Mathematics and Mathematical Sciences 17 Applied Numerical Mathematics 17 Journal of the Egyptian Mathematical Society 17 Georgian Mathematical Journal 17 Vietnam Journal of Mathematics 17 Journal of Theoretical Biology 17 Journal of Applied Analysis and Computation ...and 436 more Serials
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### Cited in 55 Fields

 6,358 Ordinary differential equations (34-XX) 2,164 Operator theory (47-XX) 971 Biology and other natural sciences (92-XX) 947 Partial differential equations (35-XX) 883 Systems theory; control (93-XX) 796 Integral equations (45-XX) 709 Real functions (26-XX) 682 Difference and functional equations (39-XX) 674 General topology (54-XX) 571 Numerical analysis (65-XX) 380 Dynamical systems and ergodic theory (37-XX) 327 Probability theory and stochastic processes (60-XX) 212 Calculus of variations and optimal control; optimization (49-XX) 116 Functional analysis (46-XX) 103 Global analysis, analysis on manifolds (58-XX) 80 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 61 Mechanics of deformable solids (74-XX) 52 Mechanics of particles and systems (70-XX) 48 Linear and multilinear algebra; matrix theory (15-XX) 48 Fluid mechanics (76-XX) 45 Operations research, mathematical programming (90-XX) 40 Computer science (68-XX) 38 Approximations and expansions (41-XX) 38 Statistical mechanics, structure of matter (82-XX) 36 Measure and integration (28-XX) 36 Special functions (33-XX) 28 Mathematical logic and foundations (03-XX) 25 Integral transforms, operational calculus (44-XX) 22 Combinatorics (05-XX) 18 Quantum theory (81-XX) 15 Order, lattices, ordered algebraic structures (06-XX) 13 General and overarching topics; collections (00-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 12 History and biography (01-XX) 11 Abstract harmonic analysis (43-XX) 11 Statistics (62-XX) 11 Information and communication theory, circuits (94-XX) 9 Number theory (11-XX) 9 Functions of a complex variable (30-XX) 9 Sequences, series, summability (40-XX) 8 Convex and discrete geometry (52-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Algebraic topology (55-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Differential geometry (53-XX) 5 Optics, electromagnetic theory (78-XX) 4 Geophysics (86-XX) 3 Topological groups, Lie groups (22-XX) 3 Potential theory (31-XX) 2 Field theory and polynomials (12-XX) 2 Geometry (51-XX) 2 Mathematics education (97-XX) 1 General algebraic systems (08-XX) 1 Category theory; homological algebra (18-XX) 1 Manifolds and cell complexes (57-XX)