Existence of two positive solutions for a class of third-order impulsive singular integro-differential equations on the half-line in Banach spaces

Dajun Guo

doi:10.1186/s13661-016-0577-8

Abstract

In this paper, we discuss the existence of two positive solutions for an infinite boundary value problem of third-order impulsive singular integro-differential equations on the half-line in Banach spaces 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
By constructing a bounded closed convex set, apart from the singularities, and using the Schauder fixed point theorem, we obtain the existence of positive solutions for the infinite boundary value problems
In a recent paper [ ], we discussed the existence of two positive solutions for a class of second order superlinear singular equations by means of different method, that is, by using the fixed point theorem of cone expansion and compression with norm type, which was established by the author in [ ]

Summary

Introduction

The theory of impulsive differential equations has been emerging as an important area of investigation in recent years (see [ – ]). Let PC [J, E] = {u ∈ PC[J, E] : u (t) is continuous at t = tk, and u (tk+) and u (tk–) exist for k = , , , .

Results

Conclusion