Periodic boundary value problems for second-order functional differential equations with impulse

Yulin Zhao,Haibo Chen,Bin Qin

doi:10.1186/1687-1847-2014-134

Abstract

In this paper, we study the existence of multiple positive solutions of the second-order periodic boundary value problems for functional differential equations with impulse. The proof of our main results is based upon the fixed point index theorem in cones.

Highlights

We will consider the existence of positive solutions for boundary value problems of second order impulsive functional differential equations of the form
Where J = [, T], f : J × Cτ → R is a continuous function, φ ∈ Cτ (Cτ be given in Section ), τ ≥, ρ(t) ∈ C(J, (, ∞)), ut ∈ Cτ, ut(θ ) = u(t + θ ), θ ∈ [–τ, ]
Many papers have been published about the existence analysis of periodic boundary value problems of first and second order for ordinary or functional or integro-differential equations with impulsive

Summary

Introduction

We will consider the existence of positive solutions for boundary value problems of second order impulsive functional differential equations of the form Many papers have been published about the existence analysis of periodic boundary value problems of first and second order for ordinary or functional or integro-differential equations with impulsive.

Objectives

Results

Conclusion