Multiple positive solutions for a nonlinear three-point integral boundary-value problem

Abstract

We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \begin{equation*} \label{eq-1} \begin{gathered} {u^{\prime \prime}}(t)+f(t, u(t))=0,\ 0<t<T, \\ u(0)=βu(η),\ u(T)=α\int_{0}^ηu(s)ds, \end{gathered} \end{equation*} where $0<\eta <T$, $0<\alpha <\frac{2T}{{\eta }^2}$, $0<\beta <\frac{2T-\alpha {\eta }^2}{\alpha {\eta }^2-2\eta +2T}$ are given constants. We establish the existence of at least three positive solutions by using the Leggett-Williams fixed-point theorem.

arXiv comment10 pages