Eigenvalues and symmetric positive solutions for a three-point boundary-value problem

Abstract

In this paper, we consider the second-order three-point boundary-value problem u′′(t) + ƒ(t, u, u′, u′′) = 0, 0 ≤ t ≤ 1, u(0) = u(1) = αu(η) Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the highest-order derivative occurs nonlinearly in our problem.