Triple positive solutions of nth order impulsive integro-differential equations

Zeyong Qiu,Shihuang Hong

doi:10.14232/ejqtde.2011.1.57

Abstract

Triple positive solutions of nth order impulsive integro-differential equations

Highlights

The branch of modern applied analysis known as ”impulsive” differential equations furnishes a natural framework to mathematically describe some ”jumping processes”
Most of the works in this area discussed the first- and second- order problems, though the theory of nth order nonlinear impulsive integro-differential equations of mixed type has received attention and some significant results have been obtained in very recent years
Guo [5] has established the existence of solutions for a class of nth order problems on infinite interval with infinite number of impulsive times in Banach spaces by means of the Schauder fixed point theorem

Summary

Introduction

The branch of modern applied analysis known as ”impulsive” differential equations furnishes a natural framework to mathematically describe some ”jumping processes”. Guo [5] has established the existence of solutions for a class of nth order problems on infinite interval with infinite number of impulsive times in Banach spaces by means of the Schauder fixed point theorem. By using the fixed point index theory of completely continuous operators, in [4] Guo has investigated the existence of twin positive solutions of a boundary value problem (BVP) for nth-order nonlinear impulsive integro-differential equation of mixed type as follows: u(n)(t) = f (t, u(t), u′(t), · · · , u(n−1)(t), (T u)(t), (Su)(t)), ∀t ∈ J′. This is an application of a new fixed point theorem introduced by Avery and Peterson [1] which has been used to verify the existence of three positive solutions for ordinary differential equations in [15] and for p-Laplacian dynamic equations on time scales in [16]

Preliminaries

Main Results

An Example

Conclusion