Edit Profile (opens in new tab) Vatsala, Aghalaya S. Compute Distance To: Compute Author ID: vatsala.aghalaya-s Published as: Vatsala, A. S.; Vatsala, Aghalaya S.; Vatsala, Aghalaya more...less External Links: MGP Documents Indexed: 150 Publications since 1973, including 2 Books Co-Authors: 67 Co-Authors with 126 Joint Publications 965 Co-Co-Authors all top 5 Co-Authors 16 single-authored 30 Lakshmikantham, Vangipuram 12 Stutson, Donna S. 10 Melton, Tanya G. 9 Vasundhara Devi, Jonnalagadda 6 Leela, Srinivasa G. 5 Denton, Zachary 5 Ladde, Gangaram S. 4 Ramírez, Juan Diego 4 Uvah, Josaphat A. 3 Bainov, Drumi Dimitrov 3 Shahzad, Naseer 3 Sowmya, M. 3 Stamova, Ivanka Milkova 3 Vaughn, R. L. 3 Wang, Liwen 3 West, Ianna H. 2 Alkahby, Hadi Yahya 2 Das, Kaustuv Mukul 2 Drici, Zahia 2 Khristova, Snezhana G. 2 Kouhestani, Nader 2 Mahrous, Mohamed A. 2 Rao, Vadrevu Sree Hari 2 Sambandham, Bhuvaneswari 2 Shendge, G. R. 2 Sokol, Michael 1 Adams, Brandi M. 1 Ahmad, Shair 1 Anderson, Vinchencia 1 Bettis, Courtney 1 Brown, Shala 1 Chandrakala, G. 1 Chellamuthu, Vinodh K. 1 Chhetri, P. G. 1 Chiquet, Ross A. 1 Davis, Jacqkis 1 Davis, Naleceia 1 Dayonna, P. 1 Epps, Paige 1 Jasmine, W. 1 Jiang, Jiahui 1 Kaul, Saroop K. 1 Koksal, Semen 1 Lakshmikanthama, V. 1 Laksmikantham, V. 1 Liu, Xinzhi 1 Liu, Yucheng 1 Lyons, Rainey 1 Marinov, Tchavdar T. 1 Miller, Frederick W. 1 Mullen, DeAndrai 1 Muniswamy, Sowmya 1 Ng, Ping Wong 1 Noël, C. 1 Oguztöreli, Mehmet Namik 1 Pachpatte, Baburao Govindrao 1 Rajalakshmi, S. G. 1 Setia, Amit 1 Sheila, H. 1 Shobha Rani, V. 1 Subedi, Subhash 1 Sun, Yong 1 Tull-Walker, Naeem 1 Vajravelu, Kuppalapalle 1 Vijesh, V. Antony 1 Zenia, N. 1 Zhao, Xiaoquan all top 5 Serials 11 Dynamic Systems and Applications 10 Applicable Analysis 10 Applied Mathematics and Computation 10 Nonlinear Studies 8 Journal of Mathematical Analysis and Applications 6 Communications in Applied Analysis 6 Nonlinear Dynamics and Systems Theory 5 Neural, Parallel & Scientific Computations 5 Nonlinear Analysis. Theory, Methods & Applications 4 Journal of Applied Mathematics and Stochastic Analysis 3 Computers & Mathematics with Applications 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Journal of Computational and Applied Mathematics 2 Rendiconti del Seminario Matematico della Università di Padova 2 Applied Mathematics Letters 2 Opuscula Mathematica 2 Journal of Difference Equations and Applications 2 Dynamics of Continuous, Discrete and Impulsive Systems 2 Boundary Value Problems 2 Mathematics 1 Journal of the Korean Mathematical Society 1 Quarterly of Applied Mathematics 1 Transactions of the American Mathematical Society 1 Journal of Integral Equations 1 Note di Matematica 1 Journal of Applied Mathematics and Simulation 1 Analele Științifice ale Universității Al. I. Cuza din Iași. Serie Nouă. Matematică 1 Facta Universitatis. Series Mechanics, Automatic Control and Robotics 1 Nonlinear Times and Digest 1 Nonlinear World 1 Journal of Inequalities and Applications 1 Neliniĭni Kolyvannya 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Mathematics and its Applications (Dordrecht) 1 International Journal of Difference Equations 1 Involve 1 International Journal of Qualitative Theory of Differential Equations and Applications 1 International Journal of Differential Equations 1 Journal of Fractional Calculus and Applications 1 Mathematical Sciences 1 Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics all top 5 Fields 101 Ordinary differential equations (34-XX) 39 Partial differential equations (35-XX) 21 Numerical analysis (65-XX) 12 Integral equations (45-XX) 11 Real functions (26-XX) 5 Systems theory; control (93-XX) 3 Difference and functional equations (39-XX) 3 Operator theory (47-XX) 3 Fluid mechanics (76-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Approximations and expansions (41-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 97 Publications have been cited 1,937 times in 1,457 Documents Cited by ▼ Year ▼ Basic theory of fractional differential equations. Zbl 1161.34001Lakshmikantham, V.; Vatsala, A. S. 493 2008 Monotone iterative techniques for nonlinear differential equations. Zbl 0658.35003Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S. 467 1985 General uniqueness and monotone iterative technique for fractional differential equations. Zbl 1161.34031Lakshmikantham, V.; Vatsala, A. S. 165 2008 Generalized quasilinearization for nonlinear problems. Zbl 0997.34501Lakshmikantham, V.; Vatsala, A. S. 119 1998 Theory of fractional differential inequalities and applications. Zbl 1159.34006Lakshmikantham, V.; Vatsala, A. S. 116 2007 Fractional integral inequalities and applications. Zbl 1189.26044Denton, Z.; Vatsala, A. S. 40 2010 Interconnection between set and fuzzy differential equations. Zbl 1029.34049Laksmikantham, V.; Leela, S.; Vatsala, A. S. 37 2003 Hybrid systems on time scales. Zbl 1032.34050Lakshmikantham, V.; Vatsala, A. S. 32 2002 Monotone iterative technique for fractional differential equations with periodic boundary conditions. Zbl 1197.26007Ramírez, J. D.; Vatsala, A. S. 28 2009 Green’s function for n-n boundary value problem and an analogue of Hartman’s result. Zbl 0312.34011Das, K. M.; Vatsala, A. S. 19 1975 Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations. Zbl 1232.34012Denton, Z.; Vatsala, A. S. 18 2011 Differential inequalities with initial time difference and applications. Zbl 0933.34007Lakshmikantham, V.; Vatsala, A. S. 17 1999 Periodic boundary value problems of impulsive differential equations. Zbl 0753.34008Vatsala, A. S.; Sun, Yong 15 1992 Generalized monotone iterative technique for Caputo fractional differential equation with periodic boundary condition via initial value problem. Zbl 1267.34011Ramírez, J. Diego; Vatsala, A. S. 15 2012 Basic theory of fuzzy difference equations. Zbl 1023.39008Lakshmikantham, V.; Vatsala, A. S. 15 2002 Existence of coupled quasi-solutions of systems of nonlinear elliptic boundary value problems. Zbl 0575.35033Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S. 15 1984 Method of quasi-upper and lower solutions in abstract cones. Zbl 0497.34047Lakshmikantham, V.; Leela, S.; Vatsala, A. S. 13 1982 Existence of coupled quasi-solutions of systems of nonlinear reaction- diffusion equations. Zbl 0589.35061Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S. 13 1985 Monotone iterative technique for semilinear elliptic systems. Zbl 1143.65388Vatsala, A. S.; Yang, Jie 11 2005 Generalized monotone iterative method for initial value problems. Zbl 1112.34304West, I. H.; Vatsala, A. S. 11 2004 Generalized quasilinearization versus Newton method. Zbl 1078.65037Lakshmikantham, V.; Vatsala, A. S. 11 2005 Set differential equations and monotone flows. Zbl 1090.34064Lakshmikantham, V.; Vatsala, A. S. 11 2003 Impulsive quenching for reaction-diffusion equations. Zbl 0810.35039Chan, C. Y.; Ke, L.; Vatsala, A. S. 10 1994 Monotone method for integrodifferential equations with periodic boundary conditions. Zbl 0605.45007Kaul, Saroop K.; Vatsala, A. S. 10 1986 Generalized quasilinearization method and higher order of convergence for second-order boundary value problems. Zbl 1135.34005Melton, Tanya G.; Vatsala, A. S. 9 2006 On Green’s function of an n-point boundary value problem. Zbl 0275.34017Das, K. M.; Vatsala, A. S. 9 1973 Monotone iterative technique for partial differential equations of first order. Zbl 0566.35016Lakshmikantham, V.; Oguztöreli, M. N.; Vatsala, A. S. 9 1984 Quasilinearization method via lower and upper solutions for Riemann-Liouville fractional differential equations. Zbl 1237.34006Denton, Z.; Ng, P. W.; Vatsala, A. S. 9 2011 Basic results for sequential Caputo fractional differential equations. Zbl 1315.34015Sambandham, Bhuvaneswari; Vatsala, Aghalaya S. 9 2015 Improved generalized quasilinearization method for second order boundary value problem. Zbl 0820.34008Shahzad, N.; Vatsala, A. S. 8 1995 Extension of the method of generalized quasilinearization for second order boundary value problems. Zbl 0831.34031Shahzad, N.; Vatsala, A. S. 8 1995 On the existence of periodic quasi-solutions for first order systems. Zbl 0526.34029Vatsala, A. S. 7 1983 Stability of moving invariant sets. Zbl 0947.34039Lakshmikantham, V.; Vatsala, A. S. 7 1997 Generalized quasilinearization for an impulsive differential equation with variable moments of impulse. Zbl 1048.34028Vasundara Devi, J.; Vatsala, A. S. 7 2003 Inverse problem for coefficient identification in the Euler-Bernoulli equation. Zbl 1155.34356Marinov, Tchavdar T.; Vatsala, Aghalaya S. 7 2008 Existence and comparison results for a class of Volterra integral equations of Sobolev type. Zbl 0458.45005Lakshmikantham, V.; Vatsala, A. S.; Vaughn, R. L. 6 1979 A unified exhaustive study of monotone iterative method for initial value problems. Zbl 1094.34503Sokol, Michael; Vatsala, A. S. 6 2001 Monotone iterative technique for impulsive set differential equations. Zbl 1080.34004Vasundhara Devi, J.; Vatsala, A. S. 6 2004 A study of set differential equations with delay. Zbl 1069.34112Vasundhara Devi, J.; Vatsala, A. S. 6 2004 Monotone method for nonlinear Caputo fractional boundary value problems. Zbl 1234.26019Ramírez, J. D.; Vatsala, A. S. 6 2011 Stability results for solutions of reaction diffusion systems by the method of quasisolutions. Zbl 0443.34024Lakshmikantham, V.; Vatsala, A. S. 5 1981 Method of generalized quasilinearization for second order boundary value problems. Zbl 0882.34026Malek, S.; Vatsala, A. S. 5 1994 Existence of fixed points of fuzzy mappings via theory of fuzzy differential equations. Zbl 0943.34051Lakshmikantham, V.; Vatsala, A. S. 4 2000 Existence and asymptotic behavior of reaction-diffusion systems via coupled quasi-solutions. Zbl 0513.35040Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S. 4 1982 Existence and comparison results for differential equations of Sobolev type. Zbl 0435.34005Vatsala, A. S.; Vaughn, R. L. 4 1980 Composite boundedness and stability results by perturbing Lyapunov functions. Zbl 0842.34057Stutson, Donna; Vatsala, A. S. 4 1996 Impulsive hybrid fuzzy differential equations. Zbl 1051.93060Vatsala, A. S. 4 2003 Picard’s iterative method for Caputo fractional differential equations with numerical results. Zbl 06898694Lyons, Rainey; Vatsala, Aghalaya S.; Chiquet, Ross A. 4 2017 Variation of parameters in terms of Lyapunov-like functions and stability of perturbed systems. Zbl 0930.34039Liu, Xinzhi; Vatsala, A. S. 3 1998 Generalized monotone technique for an impulsive differential equation with variable moments of impulse. Zbl 1022.34005Vatsala, A. S.; Vasundara Devi, J. 3 2002 Dynamic systems on time scales and generalized quasilinearization. Zbl 0873.34007Leela, S.; Vatsala, A. S. 3 1996 Global stability of sets for linear impulsive differential-difference equations with variable impulsive perturbations. Zbl 0866.34007Bainov, Drumi; Stamova, Ivanka; Vatsala, Aghalaya 3 1996 Improved generalized quasilinearization method and rapid convergence for reaction diffusion equations. Zbl 1180.65131Melton, Tanya G.; Vatsala, A. S. 3 2008 Generalized quasilinearization and semilinear elliptic boundary value problems. Zbl 0959.35062Lakshmikantham, V.; Vatsala, A. S. 3 2000 Theory of differential and integral inequalities with initial time difference and applications. Zbl 0988.34008Lakshmikantham, V.; Vatsala, A. S. 3 1999 Generalized iterative methods for Caputo fractional differential equations via coupled lower and upper solutions with superlinear convergence. Zbl 1327.34009Sowmya, M.; Vatsala, A. S. 3 2015 The quasilinearization method in the system of reaction-diffusion equations. Zbl 0943.65108Jiang, Jiahui; Vatsala, A. S. 2 1998 The method of generalized quasilinearization and its applications. Zbl 0931.34009Lakshmikantham, V.; Vatsala, A. S. 2 1999 The generalized quasi-linearization method for reaction diffusion equations on an unbounded domain. Zbl 0938.35076Vatsala, A. S.; Wang, Liwen 2 1999 Generalized quasilinearization method for first order periodic boundary value problem with fixed moments of impulses. Zbl 0934.34006Vatsala, A. S.; Shobha Rani, V.; Vasundara Devi, J. 2 1999 The present state of UAS for Volterra and delay equations. Zbl 0957.45016Lakshmikantham, V.; Vatsala, A. S. 2 2000 Existence of extremal solutions and comparison results for delay differential equations in abstract cones. Zbl 0507.34063Vatsala, A. S.; Vaughn, R. L. 2 1981 Comparison results for first and second order boundary value problems at resonance. Zbl 0542.34019Shendge, G. R.; Vatsala, A. S. 2 1983 Monotone method for equations describing transport phenomena in a Banach space. Zbl 0476.65038Pachpatte, B. G.; Vatsala, A. S. 2 1981 Strict stability criteria for dynamic systems on time scales. Zbl 0903.34050Vatsala, A. S. 2 1998 Quasilinearization for the periodic boundary value problem for systems of impulsive differential equations. Zbl 1158.34013Hristova, S. G.; Vatsala, A. S. 2 2006 Generalized quasilinearization and reaction diffusion equations. Zbl 0819.35078Vatsala, A. S. 2 1994 Monotone method for first order singular systems with boundary conditions. Zbl 0697.34015Uvah, J. A.; Vatsala, A. S. 2 1989 Quadratic and semi-quadratic convergence of IVP. Zbl 1060.65615Stutson, Donna; Vatsala, A. S. 2 1995 Stability in terms of two measures of hybrid systems with partially visible solutions. Zbl 1088.34049Lakshmikanthama, V.; Vasundhara Devi, J.; Vatsala, A. S. 2 2005 Monotone iterative technique for singular systems of differential equations. Zbl 0649.34021Vatsala, A. S. 2 1987 Generalized quasilinearization method for RL fractional differential equations. Zbl 1400.34005Denton, Z.; Vatsala, A. S. 2 2012 Quasilinearization for second order singular boundary value problems with solutions in weighted spaces. Zbl 0970.34016Vasundhara Devi, J.; Vatsala, A. S. 2 2000 Generalized monotone method for ordinary and Caputo fractional differential equations. Zbl 1336.34019Vatsala, Aghalaya S.; Sowmya, M.; Stutson, Donna S. 2 2015 Generalized monontone iterative technique for functional differential equations with retardation and anticipation. Zbl 1310.34090Vatsala, A. S. 1 2007 An extension of quasilinearization to reaction diffusion equations with fixed moments of impulses. Zbl 0952.35063Drici, Zahia; Kouhestani, Nader; Vatsala, A. S. 1 2000 Method of mixed monotony for nonlinear equations with a singular linear part. Zbl 0632.65060Lakshmikantham, V.; Vatsala, A. S. 1 1987 Comparison results of reaction-diffusion equations with delay in abstract cones. Zbl 0499.35010Ahmad, Shair; Vatsala, A. S. 1 1981 Existence of solutions for a system of second order nonlinear periodic boundary value problems. Zbl 0506.34015Rao, V. Sree Hari; Vatsala, A. S. 1 1983 Existence of coupled minimal and maximal periodic quasisolutions for systems of first order PBVP via quasisolutions. Zbl 0529.34050Vatsala, A. S. 1 1984 Monotone method for a system of second order periodic boundary value problems. Zbl 0541.34009Lakshmikantham, V.; Rao, V. Sree Hari; Vatsala, A. S. 1 1984 Generalized practical stability results by perturbing Lyapunov functions. Zbl 0851.34052Stutson, Donna; Vatsala, A. S. 1 1996 Generalized quasilinearization and first-order periodic boundary value problem. Zbl 0855.65091Vatsala, A. S.; Stutson, Donna 1 1996 Generalized monotone method for Caputo fractional differential equation with periodic boundary condition. Zbl 1227.34021Ramírez, J. Diego; Vatsala, Aghalaya S. 1 2010 The method of generalized quasilinearization in finite systems. Zbl 0901.34013Vatsala, A. S.; Shahzad, N.; Köksal, S. 1 1996 Generalized quasilinearization for impulsive reaction-diffusion equations with fixed moments of impulses. Zbl 0910.35066Drici, Zahia; Vatsala, A. S.; Kouhestani, Nader 1 1998 Method of vector Lyapunov functions for impulsive fuzzy systems. Zbl 1083.34041Vasundhara Devi, J.; Vatsala, A. S. 1 2004 Systems of first order partial differential equations and monotone iterative technique. Zbl 0582.35013Ladde, G. S.; Vatsala, A. S. 1 1985 Numerical investigation of generalized quasilinearization method for reaction diffusion systems. Zbl 1085.65084Yang, Jie; Vatsala, A. S. 1 2005 The generalized quasilinearization method for parabolic integro-differential equations. Zbl 1026.35009Vatsala, A. S.; Wang, Liwen 1 2001 Superlinear convergence via mixed generalized quasilinearization method and generalized monotone method. Zbl 1301.34018Anderson, Vinchencia; Bettis, Courtney; Brown, Shala; Davis, Jacqkis; Tull-Walker, Naeem; Chellamuthu, Vinodh; Vatsala, Aghalaya S. 1 2014 Numerical application of generalized monotone method for population models. Zbl 1278.34033Noel, C.; Sheila, H.; Zenia, N.; Dayonna, P.; Jasmine, W.; Vatsala, A. S.; Sowmya, M. 1 2012 Extended method of quasilinearization for systems of nonlinear differential equations. Zbl 1041.34006Vajravelu, K.; Vatsala, A. S. 1 2000 A quenching problem of Kawarada’s type for one dimensional Caputo fractional reaction diffusion equation. Zbl 1405.35251Subedi, Subhash; Vatsala, Aghalaya S. 1 2018 Generalized monotone method for Caputo fractional differential systems via coupled lower and upper solutions. Zbl 1236.34020Stutson, Donna; Vatsala, A. S. 1 2011 Higher order of convergence via generalized quasilinearization method for parabolic integro-differential equations. Zbl 1142.65109Melton, Tanya G.; Vatsala, A. S. 1 2007 Riemann Liouville and Caputo fractional differential and integral inequalities. Zbl 1322.34013Stutson, Donna S.; Vatsala, Aghalaya S. 1 2014 A quenching problem of Kawarada’s type for one dimensional Caputo fractional reaction diffusion equation. Zbl 1405.35251Subedi, Subhash; Vatsala, Aghalaya S. 1 2018 Picard’s iterative method for Caputo fractional differential equations with numerical results. Zbl 06898694Lyons, Rainey; Vatsala, Aghalaya S.; Chiquet, Ross A. 4 2017 Basic results for sequential Caputo fractional differential equations. Zbl 1315.34015Sambandham, Bhuvaneswari; Vatsala, Aghalaya S. 9 2015 Generalized iterative methods for Caputo fractional differential equations via coupled lower and upper solutions with superlinear convergence. Zbl 1327.34009Sowmya, M.; Vatsala, A. S. 3 2015 Generalized monotone method for ordinary and Caputo fractional differential equations. Zbl 1336.34019Vatsala, Aghalaya S.; Sowmya, M.; Stutson, Donna S. 2 2015 Superlinear convergence via mixed generalized quasilinearization method and generalized monotone method. Zbl 1301.34018Anderson, Vinchencia; Bettis, Courtney; Brown, Shala; Davis, Jacqkis; Tull-Walker, Naeem; Chellamuthu, Vinodh; Vatsala, Aghalaya S. 1 2014 Riemann Liouville and Caputo fractional differential and integral inequalities. Zbl 1322.34013Stutson, Donna S.; Vatsala, Aghalaya S. 1 2014 Generalized monotone iterative technique for Caputo fractional differential equation with periodic boundary condition via initial value problem. Zbl 1267.34011Ramírez, J. Diego; Vatsala, A. S. 15 2012 Generalized quasilinearization method for RL fractional differential equations. Zbl 1400.34005Denton, Z.; Vatsala, A. S. 2 2012 Numerical application of generalized monotone method for population models. Zbl 1278.34033Noel, C.; Sheila, H.; Zenia, N.; Dayonna, P.; Jasmine, W.; Vatsala, A. S.; Sowmya, M. 1 2012 Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations. Zbl 1232.34012Denton, Z.; Vatsala, A. S. 18 2011 Quasilinearization method via lower and upper solutions for Riemann-Liouville fractional differential equations. Zbl 1237.34006Denton, Z.; Ng, P. W.; Vatsala, A. S. 9 2011 Monotone method for nonlinear Caputo fractional boundary value problems. Zbl 1234.26019Ramírez, J. D.; Vatsala, A. S. 6 2011 Generalized monotone method for Caputo fractional differential systems via coupled lower and upper solutions. Zbl 1236.34020Stutson, Donna; Vatsala, A. S. 1 2011 Fractional integral inequalities and applications. Zbl 1189.26044Denton, Z.; Vatsala, A. S. 40 2010 Generalized monotone method for Caputo fractional differential equation with periodic boundary condition. Zbl 1227.34021Ramírez, J. Diego; Vatsala, Aghalaya S. 1 2010 Monotone iterative technique for fractional differential equations with periodic boundary conditions. Zbl 1197.26007Ramírez, J. D.; Vatsala, A. S. 28 2009 Basic theory of fractional differential equations. Zbl 1161.34001Lakshmikantham, V.; Vatsala, A. S. 493 2008 General uniqueness and monotone iterative technique for fractional differential equations. Zbl 1161.34031Lakshmikantham, V.; Vatsala, A. S. 165 2008 Inverse problem for coefficient identification in the Euler-Bernoulli equation. Zbl 1155.34356Marinov, Tchavdar T.; Vatsala, Aghalaya S. 7 2008 Improved generalized quasilinearization method and rapid convergence for reaction diffusion equations. Zbl 1180.65131Melton, Tanya G.; Vatsala, A. S. 3 2008 Theory of fractional differential inequalities and applications. Zbl 1159.34006Lakshmikantham, V.; Vatsala, A. S. 116 2007 Generalized monontone iterative technique for functional differential equations with retardation and anticipation. Zbl 1310.34090Vatsala, A. S. 1 2007 Higher order of convergence via generalized quasilinearization method for parabolic integro-differential equations. Zbl 1142.65109Melton, Tanya G.; Vatsala, A. S. 1 2007 Generalized quasilinearization method and higher order of convergence for second-order boundary value problems. Zbl 1135.34005Melton, Tanya G.; Vatsala, A. S. 9 2006 Quasilinearization for the periodic boundary value problem for systems of impulsive differential equations. Zbl 1158.34013Hristova, S. G.; Vatsala, A. S. 2 2006 Monotone iterative technique for semilinear elliptic systems. Zbl 1143.65388Vatsala, A. S.; Yang, Jie 11 2005 Generalized quasilinearization versus Newton method. Zbl 1078.65037Lakshmikantham, V.; Vatsala, A. S. 11 2005 Stability in terms of two measures of hybrid systems with partially visible solutions. Zbl 1088.34049Lakshmikanthama, V.; Vasundhara Devi, J.; Vatsala, A. S. 2 2005 Numerical investigation of generalized quasilinearization method for reaction diffusion systems. Zbl 1085.65084Yang, Jie; Vatsala, A. S. 1 2005 Generalized monotone iterative method for initial value problems. Zbl 1112.34304West, I. H.; Vatsala, A. S. 11 2004 Monotone iterative technique for impulsive set differential equations. Zbl 1080.34004Vasundhara Devi, J.; Vatsala, A. S. 6 2004 A study of set differential equations with delay. Zbl 1069.34112Vasundhara Devi, J.; Vatsala, A. S. 6 2004 Method of vector Lyapunov functions for impulsive fuzzy systems. Zbl 1083.34041Vasundhara Devi, J.; Vatsala, A. S. 1 2004 Interconnection between set and fuzzy differential equations. Zbl 1029.34049Laksmikantham, V.; Leela, S.; Vatsala, A. S. 37 2003 Set differential equations and monotone flows. Zbl 1090.34064Lakshmikantham, V.; Vatsala, A. S. 11 2003 Generalized quasilinearization for an impulsive differential equation with variable moments of impulse. Zbl 1048.34028Vasundara Devi, J.; Vatsala, A. S. 7 2003 Impulsive hybrid fuzzy differential equations. Zbl 1051.93060Vatsala, A. S. 4 2003 Hybrid systems on time scales. Zbl 1032.34050Lakshmikantham, V.; Vatsala, A. S. 32 2002 Basic theory of fuzzy difference equations. Zbl 1023.39008Lakshmikantham, V.; Vatsala, A. S. 15 2002 Generalized monotone technique for an impulsive differential equation with variable moments of impulse. Zbl 1022.34005Vatsala, A. S.; Vasundara Devi, J. 3 2002 A unified exhaustive study of monotone iterative method for initial value problems. Zbl 1094.34503Sokol, Michael; Vatsala, A. S. 6 2001 The generalized quasilinearization method for parabolic integro-differential equations. Zbl 1026.35009Vatsala, A. S.; Wang, Liwen 1 2001 Existence of fixed points of fuzzy mappings via theory of fuzzy differential equations. Zbl 0943.34051Lakshmikantham, V.; Vatsala, A. S. 4 2000 Generalized quasilinearization and semilinear elliptic boundary value problems. Zbl 0959.35062Lakshmikantham, V.; Vatsala, A. S. 3 2000 The present state of UAS for Volterra and delay equations. Zbl 0957.45016Lakshmikantham, V.; Vatsala, A. S. 2 2000 Quasilinearization for second order singular boundary value problems with solutions in weighted spaces. Zbl 0970.34016Vasundhara Devi, J.; Vatsala, A. S. 2 2000 An extension of quasilinearization to reaction diffusion equations with fixed moments of impulses. Zbl 0952.35063Drici, Zahia; Kouhestani, Nader; Vatsala, A. S. 1 2000 Extended method of quasilinearization for systems of nonlinear differential equations. Zbl 1041.34006Vajravelu, K.; Vatsala, A. S. 1 2000 Differential inequalities with initial time difference and applications. Zbl 0933.34007Lakshmikantham, V.; Vatsala, A. S. 17 1999 Theory of differential and integral inequalities with initial time difference and applications. Zbl 0988.34008Lakshmikantham, V.; Vatsala, A. S. 3 1999 The method of generalized quasilinearization and its applications. Zbl 0931.34009Lakshmikantham, V.; Vatsala, A. S. 2 1999 The generalized quasi-linearization method for reaction diffusion equations on an unbounded domain. Zbl 0938.35076Vatsala, A. S.; Wang, Liwen 2 1999 Generalized quasilinearization method for first order periodic boundary value problem with fixed moments of impulses. Zbl 0934.34006Vatsala, A. S.; Shobha Rani, V.; Vasundara Devi, J. 2 1999 Generalized quasilinearization for nonlinear problems. Zbl 0997.34501Lakshmikantham, V.; Vatsala, A. S. 119 1998 Variation of parameters in terms of Lyapunov-like functions and stability of perturbed systems. Zbl 0930.34039Liu, Xinzhi; Vatsala, A. S. 3 1998 The quasilinearization method in the system of reaction-diffusion equations. Zbl 0943.65108Jiang, Jiahui; Vatsala, A. S. 2 1998 Strict stability criteria for dynamic systems on time scales. Zbl 0903.34050Vatsala, A. S. 2 1998 Generalized quasilinearization for impulsive reaction-diffusion equations with fixed moments of impulses. Zbl 0910.35066Drici, Zahia; Vatsala, A. S.; Kouhestani, Nader 1 1998 Stability of moving invariant sets. Zbl 0947.34039Lakshmikantham, V.; Vatsala, A. S. 7 1997 Composite boundedness and stability results by perturbing Lyapunov functions. Zbl 0842.34057Stutson, Donna; Vatsala, A. S. 4 1996 Dynamic systems on time scales and generalized quasilinearization. Zbl 0873.34007Leela, S.; Vatsala, A. S. 3 1996 Global stability of sets for linear impulsive differential-difference equations with variable impulsive perturbations. Zbl 0866.34007Bainov, Drumi; Stamova, Ivanka; Vatsala, Aghalaya 3 1996 Generalized practical stability results by perturbing Lyapunov functions. Zbl 0851.34052Stutson, Donna; Vatsala, A. S. 1 1996 Generalized quasilinearization and first-order periodic boundary value problem. Zbl 0855.65091Vatsala, A. S.; Stutson, Donna 1 1996 The method of generalized quasilinearization in finite systems. Zbl 0901.34013Vatsala, A. S.; Shahzad, N.; Köksal, S. 1 1996 Improved generalized quasilinearization method for second order boundary value problem. Zbl 0820.34008Shahzad, N.; Vatsala, A. S. 8 1995 Extension of the method of generalized quasilinearization for second order boundary value problems. Zbl 0831.34031Shahzad, N.; Vatsala, A. S. 8 1995 Quadratic and semi-quadratic convergence of IVP. Zbl 1060.65615Stutson, Donna; Vatsala, A. S. 2 1995 Impulsive quenching for reaction-diffusion equations. Zbl 0810.35039Chan, C. Y.; Ke, L.; Vatsala, A. S. 10 1994 Method of generalized quasilinearization for second order boundary value problems. Zbl 0882.34026Malek, S.; Vatsala, A. S. 5 1994 Generalized quasilinearization and reaction diffusion equations. Zbl 0819.35078Vatsala, A. S. 2 1994 Periodic boundary value problems of impulsive differential equations. Zbl 0753.34008Vatsala, A. S.; Sun, Yong 15 1992 Monotone method for first order singular systems with boundary conditions. Zbl 0697.34015Uvah, J. A.; Vatsala, A. S. 2 1989 Monotone iterative technique for singular systems of differential equations. Zbl 0649.34021Vatsala, A. S. 2 1987 Method of mixed monotony for nonlinear equations with a singular linear part. Zbl 0632.65060Lakshmikantham, V.; Vatsala, A. S. 1 1987 Monotone method for integrodifferential equations with periodic boundary conditions. Zbl 0605.45007Kaul, Saroop K.; Vatsala, A. S. 10 1986 Monotone iterative techniques for nonlinear differential equations. Zbl 0658.35003Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S. 467 1985 Existence of coupled quasi-solutions of systems of nonlinear reaction- diffusion equations. Zbl 0589.35061Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S. 13 1985 Systems of first order partial differential equations and monotone iterative technique. Zbl 0582.35013Ladde, G. S.; Vatsala, A. S. 1 1985 Existence of coupled quasi-solutions of systems of nonlinear elliptic boundary value problems. Zbl 0575.35033Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S. 15 1984 Monotone iterative technique for partial differential equations of first order. Zbl 0566.35016Lakshmikantham, V.; Oguztöreli, M. N.; Vatsala, A. S. 9 1984 Existence of coupled minimal and maximal periodic quasisolutions for systems of first order PBVP via quasisolutions. Zbl 0529.34050Vatsala, A. S. 1 1984 Monotone method for a system of second order periodic boundary value problems. Zbl 0541.34009Lakshmikantham, V.; Rao, V. Sree Hari; Vatsala, A. S. 1 1984 On the existence of periodic quasi-solutions for first order systems. Zbl 0526.34029Vatsala, A. S. 7 1983 Comparison results for first and second order boundary value problems at resonance. Zbl 0542.34019Shendge, G. R.; Vatsala, A. S. 2 1983 Existence of solutions for a system of second order nonlinear periodic boundary value problems. Zbl 0506.34015Rao, V. Sree Hari; Vatsala, A. S. 1 1983 Method of quasi-upper and lower solutions in abstract cones. Zbl 0497.34047Lakshmikantham, V.; Leela, S.; Vatsala, A. S. 13 1982 Existence and asymptotic behavior of reaction-diffusion systems via coupled quasi-solutions. Zbl 0513.35040Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S. 4 1982 Stability results for solutions of reaction diffusion systems by the method of quasisolutions. Zbl 0443.34024Lakshmikantham, V.; Vatsala, A. S. 5 1981 Existence of extremal solutions and comparison results for delay differential equations in abstract cones. Zbl 0507.34063Vatsala, A. S.; Vaughn, R. L. 2 1981 Monotone method for equations describing transport phenomena in a Banach space. Zbl 0476.65038Pachpatte, B. G.; Vatsala, A. S. 2 1981 Comparison results of reaction-diffusion equations with delay in abstract cones. Zbl 0499.35010Ahmad, Shair; Vatsala, A. S. 1 1981 Existence and comparison results for differential equations of Sobolev type. Zbl 0435.34005Vatsala, A. S.; Vaughn, R. L. 4 1980 Existence and comparison results for a class of Volterra integral equations of Sobolev type. Zbl 0458.45005Lakshmikantham, V.; Vatsala, A. S.; Vaughn, R. L. 6 1979 Green’s function for n-n boundary value problem and an analogue of Hartman’s result. Zbl 0312.34011Das, K. M.; Vatsala, A. S. 19 1975 On Green’s function of an n-point boundary value problem. Zbl 0275.34017Das, K. M.; Vatsala, A. S. 9 1973 all cited Publications top 5 cited Publications all top 5 Cited by 1,507 Authors 60 Nieto Roig, Juan Jose 46 Agarwal, Ravi P. 44 Lakshmikantham, Vangipuram 43 Jankowski, Tadeusz 34 Vatsala, Aghalaya S. 29 Ahmad, Bashir 26 Băleanu, Dumitru I. 26 Cabada, Alberto 25 Wang, Guotao 23 Wang, Peiguang 20 O’Regan, Donal 19 Rodríguez-López, Rosana 17 Wu, Yonghong 17 Zhang, Lihong 15 Benchohra, Mouffak 14 Liu, Lishan 13 Khan, Rahmat Ali 13 Shen, Jianhua 13 Vasundhara Devi, Jonnalagadda 13 Zhou, Yong 12 Khristova, Snezhana G. 12 Li, Yongkun 12 Li, Yongxiang 12 Ntouyas, Sotiris K. 12 Pao, Chia-Ven 11 Carl, Siegfried 11 Jiang, Daqing 11 Liu, Zhenhai 10 Akhmet, Marat Ubaydulla 10 Leela, Srinivasa G. 10 Liang, Sihua 10 Malinowski, Marek T. 10 N’Guérékata, Gaston Mandata 10 Shah, Kamal 9 Agarwal, Praveen 9 Al-saedi, Ahmed Eid Salem 9 Kucche, Kishor D. 9 McRae, Farzana A. 9 Sivasundaram, Seenith 9 Yakar, Coskun 8 Bai, Zhanbing 8 Chen, Pengyu 8 Eloe, Paul W. 8 He, Zhimin 8 Liu, Xinzhi 8 Nyamoradi, Nemat 8 Salahshour, Soheil 8 Samet, Bessem 8 Tariboon, Jessada 8 Zhang, Jihui 7 Abdeljawad, Thabet 7 Afrouzi, Ghasem Alizadeh 7 Ardjouni, Abdelouaheb 7 Bainov, Drumi Dimitrov 7 Bhaskar, Tenali Gnana 7 Cuevas, Claudio 7 Cui, Yujun 7 Deng, Keng 7 Djoudi, Ahcene 7 El-Gebeily, Mohamed A. 7 Henderson, Johnny Lee 7 Hilal, Khalid 7 Kamont, Zdzisław 7 Li, An 7 Luo, Zhiguo 7 Lv, Zhiwei 7 Michta, Mariusz 7 Wang, Weibing 7 Wang, Yuanming 6 Drici, Zahia 6 Ge, Weigao 6 Guo, Limin 6 Hamani, Samira 6 Han, Zhenlai 6 Hong, Shihuang 6 Jiao, Feng 6 Ladde, Gangaram S. 6 Li, Yong 6 Liz, Eduardo 6 López Pouso, Rodrigo 6 Mophou, Gisèle Massengo 6 Song, Guangxing 6 Sun, Ji Tao 6 Vajravelu, Kuppalapalle 6 Zhang, Shuqin 5 Ahmadian, Ali 5 Babakhani, Azizollah 5 Cao, Jinde 5 Chen, Yubo 5 Ding, Xiaoli 5 Erbe, Lynn Harry 5 Jiang, Wei 5 Jiang, Weihua 5 Lachouri, Adel 5 Liu, Yuji 5 Lupulescu, Vasile 5 Merdivenci Atici, Ferhan 5 Minchev, Emil 5 Ouahab, Abdelghani 5 Ouyang, Zigen ...and 1,407 more Authors all top 5 Cited in 228 Serials 130 Applied Mathematics and Computation 106 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 92 Computers & Mathematics with Applications 90 Advances in Difference Equations 80 Journal of Mathematical Analysis and Applications 59 Abstract and Applied Analysis 57 Nonlinear Analysis. Theory, Methods & Applications 50 Journal of Computational and Applied Mathematics 43 Boundary Value Problems 29 Applicable Analysis 26 Journal of Applied Mathematics and Computing 25 Applied Mathematics Letters 22 Nonlinear Analysis. 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Series Mathematics and Informatics ...and 128 more Serials all top 5 Cited in 42 Fields 1,035 Ordinary differential equations (34-XX) 250 Operator theory (47-XX) 236 Partial differential equations (35-XX) 214 Real functions (26-XX) 165 Numerical analysis (65-XX) 145 Integral equations (45-XX) 63 Systems theory; control (93-XX) 60 Difference and functional equations (39-XX) 60 Biology and other natural sciences (92-XX) 35 Probability theory and stochastic processes (60-XX) 19 Dynamical systems and ergodic theory (37-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 16 Special functions (33-XX) 16 Global analysis, analysis on manifolds (58-XX) 10 General topology (54-XX) 10 Mechanics of deformable solids (74-XX) 8 Mathematical logic and foundations (03-XX) 6 Approximations and expansions (41-XX) 6 Functional analysis (46-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Combinatorics (05-XX) 5 Measure and integration (28-XX) 5 Abstract harmonic analysis (43-XX) 5 Mechanics of particles and systems (70-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Fluid mechanics (76-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral transforms, operational calculus (44-XX) 3 Statistics (62-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Quantum theory (81-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year