Existence of Solutions for m-point Boundary Value Problems on a Half-Line

Abstract

By using the Leray-Schauder continuation theorem, we establish the existence of solutions for m-point boundary value problems on a half-line x″(t)+f(t,x(t),x′(t))=0, 0<t<+∞, x(0)=∑i=1m−2αix(ηi),lim⁡t→+∞x′(t)=0, where αi∈R,∑i=1m−2αi≠1 and 0<η1<η2<⋯<ηm−2<+∞ are given.