Existence of positive solutions for a three-point integral boundary-value problem

Abstract

In this paper, by using the Krasnosel'skii's fixed-point theorem, we study the existence of at least one or two positive solutions to the three-point integral boundary value problem {equation*} \label{eq-1} {gathered} {u^{\prime \prime}}(t)+a(t)f(u(t))=0,\ 0<t<T, u(0)=βu(η),\ u(T)=α\int_{0}^ηu(s)ds, {gathered} {equation*} where $0<\eta <T$, $0<\alpha <\frac{2T}{{\eta }^2}$, $0\le \beta <\frac{2T-\alpha {\eta }^2}{\alpha {\eta }^2-2\eta +2T}$ are given constants.

arXiv comment13 pages; (v6): added some references