Abstract

In this paper, the author discusses the existence of two positive solutions for an infinite boundary value problem of second order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

Highlights

  • 1 Introduction The theory of impulsive differential equations has been emerging as an important area of investigation in recent years

  • Many problems have been investigated for impulsive differential equations, impulsive functional differential equations and impulsive differential inclusions

  • There is a vast literature on existence of solutions: by using upper and lower solutions together with the monotone iterative technique to obtain the extremal solutions [ – ]; by using fixed point theorems to obtain the existence of solution and multiple solutions [ – ]; by using the Leray-Schauder degree theory or fixed point index theory to obtain multiple solutions [ – ]; by using the variational method to obtain the existence of solution and existence of infinite many solutions [ – ]

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Summary

Introduction

The theory of impulsive differential equations has been emerging as an important area of investigation in recent years (see [ – ]). In recent article [ ], the author discussed the existence of two positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type, which was established by the author in [ ] (see [ – ]). It is clear: if condition (H ) is satisfied, ( ) implies ( ).

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