Quasilinearization for the periodic boundary value problem for systems of impulsive differential equations
type: Item
instance of: scholarly article
title: Quasilinearization for the periodic boundary value problem for systems of impulsive differential equations
zbMATH Open document ID: 1158.34013
DOI: 10.1155/JAMSA/2006/98318
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2007-03-19T00:00:00Z
full work available at URL: https://eudml.org/doc/55211
review text: The authors consider the system of nonlinear impulsive differential equations \[ \begin{aligned} &x'(t) = f(t,x(t)) + g(t,x(t)) \text{ for } t \in [0,T]\setminus\{t_1,\dots,t_p\}, \\ &x(\tau_k + 0) = I_k(x(\tau_k)) + G_k(x(\tau_k))\text{ for } k = 1,\ldots,p,\\ &x(0) = x(T), \end{aligned} \] where \(0 < t_1 < \cdots < t_p < T\); \(f,g : [0,T] \times {\mathbb R}^n \to {\mathbb R}^n\); \(I_k\), \(G_k : {\mathbb R}^n \to {\mathbb R}^n\) are continuous for \(i = 1,\ldots,k\). Sufficient conditions for the existence of a unique solution of the BVP are found. The proofs are based on quasilinearization and lower and upper solutions method.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 5134584
zbMATH Keywords: system of nonlinear differential equations
zbMATH Keywords: impulses
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: quasilinearization
author: Snezhana Hristova
author: Aghalaya S. Vatsala
MaRDI profile type: Publication
cites work: The method of quasilinearization for the periodic boundary value problem for systems of impulsive differential equations.
cites work: Q5514046
cites work: Quasilinearization of a boundary value problem for impulsive differential equations
cites work: An extension of the method of quasilinearization
cites work: Q3995625
cites work: Q4844226
cites work: Methods of generalized quasilinearization for periodic boundary value problems
cites work: Q4397695
cites work: Q4853771
description: scientific article; zbMATH DE number 5134584