Positive solutions of a nonlinear three-point boundary value problem with integral boundary conditions

Abstract

In this paper, by using Krasnoselskii's fixed point theorem in a cone, we study the existence of single and multiple positive solutions to the three-point integral boundary value problem (BVP) \begin{equation*} \label{eq-1} \begin{gathered} {u^{\prime \prime}}(t)+a(t)f(u(t))=0, 0<t<T, u^{\prime}(0)=0, \ u(T)={\alpha}\int_{0}^{\eta}u(s)ds, \end{gathered} \end{equation*} where $0<{\eta}<T$, $0<{\alpha}< \frac{1}{{\eta}}$, are given constants.