The existence of solutions of periodic BVP for second order impulsive differential equations

Jingli Xie,Zhiguo Luo

doi:10.1186/1029-242x-2013-406

Abstract

In this paper, we study the existence of solutions of periodic boundary value problems for impulsive differential equations depending on a parameter λ. By employing an existing critical point theorem, we find the range of the control parameter in which the boundary value problem admits at least one non-zero weak solution. An example illustrates our results. MSC:34B15, 34B18, 34B37, 58E30.

Highlights

1 Introduction The well-known impulsive differential equations serve as basic models to study the dynamics of processes that are subject to sudden changes in their states, which are often investigated in various fields of science and technology [ – ]
In the last few years, some researchers have gradually paid more attention to applying variational methods to deal with the existence of solutions for impulsive differential equation boundary value problems [ – ]
In Section, under suitable hypotheses, we prove that problem ( . ) possesses at least one non-zero weak solution when λ lies in an exactly determined open interval

Summary

Introduction

The well-known impulsive differential equations serve as basic models to study the dynamics of processes that are subject to sudden changes in their states, which are often investigated in various fields of science and technology [ – ]. This motivates us to consider the following particular periodic boundary value problems: In the last few years, some researchers have gradually paid more attention to applying variational methods to deal with the existence of solutions for impulsive differential equation boundary value problems [ – ].

Results

Conclusion