zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type. (English) Zbl 1179.45008
The authors discuss the existence of minimal and maximal solutions for a class of first order nonlinear impulsive functional integro-differential equations of mixed type with anti-periodic boundary conditions. Keeping in view the importance of functional integro-differential equations and anti-periodic boundary conditions, they apply the monotone iterative technique (MIT) to prove the existence of extremal solutions for a first order nonlinear impulsive functional integro-differential equation of mixed type with anti-periodic boundary conditions. The MIT coupled with the method of upper and lower solutions manifests itself as an effective and flexible mechanism that offers theoretical as well as constructive existence results in a closed set, generated by the lower and upper solutions.

MSC:
45J05Integro-ordinary differential equations
45L05Theoretical approximation of solutions of integral equations
45G10Nonsingular nonlinear integral equations
WorldCat.org
Full Text: DOI
References:
[1] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations. (1989) · Zbl 0719.34002
[2] Zavalishchin, S. T.; Sesekin, A. N.: Dynamic impulse systems. Theory applications. (1997) · Zbl 0880.46031
[3] Rogovchenko, Y. V.: Impulsive evolution systems: Main results and new trends. Dyn. contin. Discrete impuls. Syst. 3, 57-88 (1997) · Zbl 0879.34014
[4] Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations. (1995) · Zbl 0837.34003
[5] Zhang, W.; Fan, M.: Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays. Math. comput. Modelling 39, 479-493 (2004) · Zbl 1065.92066
[6] Yan, J.; Zhao, A.; Nieto, J. J.: Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems. Math. comput. Modelling 40, 509-518 (2004) · Zbl 1112.34052
[7] Li, W.; Huo, H.: Global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics. J. comput. Appl. math. 174, 227-238 (2005) · Zbl 1070.34089
[8] Tang, S.; Chen, L.: Density-dependent birth rate, birth pulses and their population dynamic consequences. J. math. Biol. 44, 185-199 (2002) · Zbl 0990.92033
[9] Zhang, X.; Shuai, Z.; Wang, K.: Optimal impulsive harvesting policy for single population. Nonlinear anal. RWA 4, 639-651 (2003) · Zbl 1011.92052
[10] D’onofrio, A.: On pulse vaccination strategy in the SIR epidemic model with vertical transmission. Appl. math. Lett. 18, 729-732 (2005) · Zbl 1064.92041
[11] Gao, S.; Chen, L.; Nieto, J. J.; Torres, A.: Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. Vaccine 24, 6037-6045 (2006)
[12] Choisy, M.; Guegan, J. F.; Rohani, P.: Dynamics of infectious diseases and pulse vaccination: teasing apart the embedded resonance effects. Physica D: Nonlinear phenomena 22, 26-35 (2006) · Zbl 1110.34031
[13] Wang, W.; Wang, H.; Li, Z.: The dynamic complexity of a three-species beddington-type food chain with impulsive control strategy. Chaos solitons fractals 32, 1772-1785 (2007) · Zbl 1195.92066
[14] Liu, X.; Guo, D.: Initial value problems for first order impulsive integro-differential equations in Banach spaces. Comm. appl. Nonlinear anal. 2, 65-83 (1995) · Zbl 0858.34068
[15] Lakshmikantham, V.; Rao, M. R. M.: Theory of integro-differential equations. (1995) · Zbl 0849.45004
[16] Guo, D.: Initial value problems for nonlinear second order impulsive integro-differential equations in Banach spaces. J. math. Anal. appl. 200, 1-13 (1996) · Zbl 0851.45012
[17] Guo, D.; Lakshmikantham, V.; Liu, X.: Nonlinear integral equations in abstract spaces. (1996) · Zbl 0866.45004
[18] Liu, L. S.; Wu, C. X.; Guo, F.: A unique solution of initial value problems for first order impulsive integro-differential equations of mixed type in Banach spaces. J. math. Anal. appl. 275, 369-385 (2002) · Zbl 1014.45007
[19] Nieto, J. J.; Rodrguez-Lpez, R.: New comparison results for impulsive integro-differential equations and applications. J. math. Anal. appl. 328, 1343-1368 (2007) · Zbl 1113.45007
[20] Guo, D.: Existence of positive solutions for nth-order nonlinear impulsive singular integro-differential equations in Banach spaces. Nonlinear anal. 68, 2727-2740 (2008) · Zbl 1140.45017
[21] Okochi, H.: On the existence of periodic solutions to nonlinear abstract equations. J. math. Soc. Japan 40, 541-553 (1988) · Zbl 0679.35046
[22] Okochi, H.: On the existence of anti-periodic solutions to nonlinear parabolic equations in noncylindrical domains. Nonlinear anal. 14, 771-783 (1990) · Zbl 0715.35091
[23] Aftabizadeh, A. R.; Aizicovici, S.; Pavel, N. H.: On a class of second-order anti-periodic boundary value problems. J. math. Anal. appl. 171, 301-320 (1992) · Zbl 0767.34047
[24] Chen, Y. Q.; Wang, X. D.; Xu, H. X.: Anti-periodic solutions for semilinear evolution equations. J. math. Anal. appl. 273, 627-636 (2002) · Zbl 1055.34113
[25] Luo, Z. G.; Shen, J. H.; Nieto, J. J.: Anti-periodic boundary value problem for first-order impulsive ordinary differential equations. Comput. math. Appl. 49, 253-261 (2005) · Zbl 1084.34018
[26] Y. Chen, J.J. Nieto, D. O’Regan, Antiperiodic solutions for fully nonlinear first-order differential equations, Math. Comput. Modelling (2007) in press (doi:10.1016/j.mcm.2006.12.006)
[27] Abdurrahman, A.; Anton, F.; Bordes, J.: Half-string oscillator approach to string field theory (Ghost sector: I). Nucl. phys. B 397, 260-282 (1993) · Zbl 1049.81572
[28] Li, D. S.; Zang, Z. L.: Periodic viscosity solutions of fully nonlinear first-order differential equations. J. math. Res. exposition 15, 13-16 (1995) · Zbl 0883.34006
[29] Ahn, C.; Rim, C.: Boundary flows in general coset theories. J. phys. A 32, 2509-2525 (1999) · Zbl 0960.81062
[30] Pinsky, S.; Tritman, U.: Anti-periodic boundary conditions to supersymmetric discrete light cone quantization. Phys. rev. D 087701, 4 (2000)
[31] Cabada, A.; Vivero, D. R.: Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations. Adv. differential equations 4, 291-310 (2004) · Zbl 1083.39017
[32] Wang, Y.; Shi, Y. M.: Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions. J. math. Anal. appl. 309, 56-69 (2005) · Zbl 1083.39019
[33] Delvos, F. J.; Knoche, L.: Lacunary interpolation by antiperiodic trigonometric polynomials. Bit 39, 439-450 (1999) · Zbl 0931.42003
[34] Du, J. Y.; Han, H. L.; Gin, G. X.: On trigonometric and paratrigonometric Hermite interpolation. J. approx. Theory 131, 74-99 (2004) · Zbl 1064.42002
[35] Chen, H. L.: Antiperiodic wavelets. J. comput. Math. 14, 32-39 (1996) · Zbl 0839.42014
[36] Djiakov, P.; Mityagin, B.: Spectral gaps of the periodic Schrödinger operator when its potential is an entire function. Adv. appl. Math. 31, 562-596 (2003) · Zbl 1047.34100
[37] Djiakov, P.; Mityagin, B.: Simple and double eigenvalues of the Hill operator with a two-term potential. J. approx. Theory 135, 70-104 (2005) · Zbl 1080.34066
[38] Ding, W.; Xing, Y.; Han, M.: Antiperiodic boundary value problems for first order impulsive functional differential equations. Appl. math. Comput. 186, 45-53 (2007) · Zbl 1124.34039
[39] Ahmad, B.; Nieto, J. J.: Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions. Nonlinear anal. 69, 3291-3298 (2008) · Zbl 1158.34049
[40] Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S.: Monotone iterative techniques for nonlinear differential equations. (1985) · Zbl 0658.35003
[41] Jiang, D.; Nieto, Juan J.; Zuo, W.: On monotone method for first order and second order periodic boundary value problems and periodic solutions of functional differential equations. J. math. Anal. appl. 289, 691-699 (2004) · Zbl 1134.34322
[42] Vatsala, A. S.; Yang, J.: Monotone iterative technique for semilinear elliptic systems. Bound. value probl. 2, 93-106 (2005) · Zbl 1143.65388
[43] Drici, Z.; Mcrae, F. A.; Devi, J. Vasundhara: Monotone iterative technique for periodic boundary value problems with causal operators. Nonlinear anal. 64, 1271-1277 (2006) · Zbl 1208.34103
[44] Nieto, J. J.; Rodriguez-Lopez, R.: Monotone method for first-order functional differential equations. Comput. math. Appl. 52, 471-484 (2006) · Zbl 1140.34406
[45] Ahmad, B.; Sivasundaram, S.: The monotone iterative technique for impulsive hybrid set valued integro-differential equations. Nonlinear anal. 65, 2260-2276 (2006) · Zbl 1111.45006
[46] Li, Y.; Liu, Z.: Monotone iterative technique for addressing impulsive integro-differential equations in Banach spaces. Nonlinear anal. 66, 83-92 (2007) · Zbl 1109.34005
[47] Ahmad, B.; Nieto, J. J.: The monotone iterative technique for three-point second-order integro-differential boundary value problems with p-Laplacian. Bound. value probl. 2007, 9 pages (2007) · Zbl 1149.65098