Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions

This paper describes the method of quasilinearization for first-order nonlinear impulsive functional differential equations with anti-periodic boundary conditions. A monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions convergin...

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Published in:	Nonlinear analysis Vol. 69; no. 10; pp. 3291 - 3298
Main Authors:	Ahmad, Bashir, Nieto, Juan J.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Ltd 15.11.2008 Elsevier
Subjects:	Difference and functional equations, recurrence relations Exact sciences and technology Finite differences and functional equations Impulsive functional differential equations Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Quadratic convergence Quasilinearization Sciences and techniques of general use 34A37 Quadratic convergence Quasilinearization 34B10 Impulsive functional differential equations Approximation Differential equation Existence of solution Nonlinear analysis Functional equation Impulsive equation Boundary condition Convergence Non linear equation Mathematical model
ISSN:	0362-546X, 1873-5215
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Abstract	This paper describes the method of quasilinearization for first-order nonlinear impulsive functional differential equations with anti-periodic boundary conditions. A monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand.
AbstractList	This paper describes the method of quasilinearization for first-order nonlinear impulsive functional differential equations with anti-periodic boundary conditions. A monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand.
Author	Ahmad, Bashir Nieto, Juan J.
Author_xml	– sequence: 1 givenname: Bashir surname: Ahmad fullname: Ahmad, Bashir email: bashir_qau@yahoo.com organization: Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. Box. 80203, Jeddah 21589, Saudi Arabia – sequence: 2 givenname: Juan J. surname: Nieto fullname: Nieto, Juan J. email: amnieto@usc.es organization: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain
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Keywords	34A37 Quadratic convergence Quasilinearization 34B10 Impulsive functional differential equations Approximation Differential equation Existence of solution Nonlinear analysis Functional equation Impulsive equation Boundary condition Convergence Non linear equation Mathematical model
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Snippet	This paper describes the method of quasilinearization for first-order nonlinear impulsive functional differential equations with anti-periodic boundary...
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SubjectTerms	Difference and functional equations, recurrence relations Exact sciences and technology Finite differences and functional equations Impulsive functional differential equations Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Quadratic convergence Quasilinearization Sciences and techniques of general use
Title	Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions
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