Existence of solutions for weighted p(r)-Laplacian impulsive system mixed type boundary value problems

Li Yin,Qihu Zhang,Guizhen Zhi,Yunrui Guo

doi:10.1186/1687-2770-2011-42

Abstract

Abstract This paper investigates the existence of solutions for weighted p(r)-Laplacian impulsive system mixed type boundary value problems. The proof of our main result is based upon Gaines and Mawhin's coincidence degree theory. Moreover, we obtain the existence of nonnegative solutions.

Highlights

1 Introduction In this paper, we mainly consider the existence of solutions for the weighted p(r)Laplacian system
In [24,25], the present author investigates the existence of solutions of p(r)-Laplacian impulsive differential equation (1-3) with periodic-like or multi-point boundary value conditions
The proof of our main result is based upon Gaines and Mawhin’s coincidence degree theory

Summary

Introduction

We mainly consider the existence of solutions for the weighted p(r)Laplacian system. On the Laplacian impulsive differential equation boundary value problems, there are many results (see [29,30,31,32,33,34,35,36,37]). Because of the nonlinearity of -Δp, results on the existence of solutions for p-Laplacian impulsive differential equation boundary value problems are rare (see [38,39]). In [24,25], the present author investigates the existence of solutions of p(r)-Laplacian impulsive differential equation (1-3) with periodic-like or multi-point boundary value conditions. We consider the existence of solutions for the weighted p(r)-Laplacian impulsive differential system mixed type boundary value condition problems, when p(r) is a general function. In the third section, we give the existence of solutions and nonnegative solutions of system (1)-(4)

Preliminary Let X and Y be two Banach spaces and L

Examples