Existence of solutions of boundary value problems for functional differential equations

Abstract

In this paper, using a simple and classical application of the Leray-Schauder degree theory, we study the existence of solutions of the following boundary value problem for functional differential equations x″(t)+f(t,xt,x′(t))=0,   t∈[0,T]x0+αx′(0)=hx(T)+βx′(T)=η where f∈C([0,T]×Cr×ℝn,ℝn), h∈Cr, η∈ℝn and α, β, are real constants.