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 $$displaylines{ u''(t)+f(t,u,u',u'')=0,quad 0leq tleq 1,cr u(0)=u(1)=alpha u(eta). }$$ 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.

Keywords

• Symmetric positive solution
• three-point boundary-value problem
• Schauder fixed point theorem
• eigenvalue.