Existence of solutions for second order impulsive differential equations
type: Item
instance of: scholarly article
title: Existence of solutions for second order impulsive differential equations
zbMATH Open document ID: 0885.34018
published in: Applied Mathematics. Series B (English Edition)
publication date: 1998-03-30T00:00:00Z
review text: The author investigates the existence of solutions of the following periodic boundary value problem for second order differential equations with impulses at fixed moments: \[ x''(t)= f(t,x(t),x'(t)), \] \[ t\neq t_{1}; \quad x(t_{1}^{+})=I(x(t_{1}),x'(t_{1}^{-})); \quad x'(t_{1}^{+})=x'(t_{1}^{-}); \quad x(0)=x(T); \quad x'(0)=x'(T), \] where \(t_{1}\in (0,T)\), and \(f:[0,T]\times \mathbb{R}^{2}\rightarrow \mathbb{R}\), \(I:\mathbb{R}^{2}\rightarrow \mathbb{R}\) are continuous functions. An equivalent abstract equation to this problem is found and then an existence result is proved by using topological degree theory. The author also gives an example to illustrate the main result of the paper.
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1078265
zbMATH Keywords: differential equations with impulses
zbMATH Keywords: degree theory
zbMATH Keywords: periodic boundary value problem
author: Zhitao Zhang
MaRDI profile type: Publication
full work available at URL: s11766-997-0032-9
OpenAlex ID: W64167452
cites work: Q4904467
cites work: Coincidence degree, and nonlinear differential equations
cites work: Extremal solutions of nonlinear impulsive integrodifferential equations in Banach spaces
cites work: Existence of solutions of boundary value problems for nonlinear second order impulsive differential equations in Banach spaces
cites work: Q3995625
cites work: Q4848134
DOI: 10.1007/S11766-997-0032-9
description: scientific article; zbMATH DE number 1078265