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)=α\int_{0}^ηu(s)ds, \end{gathered} \end{equation*} where $0<\eta <T$, $0<\alpha <\frac{1}{\eta }$, are given constants.

arXiv commentCorrections of minor typographic errors. arXiv admin note: substantial text overlap with arXiv:1304.5644. substantial text overlap with arXiv:1304.5644