Positive solutions of three-point nonlinear second order boundary value problem

Abstract

In this paper we apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive solutions to the three-point nonlinear second order boundary value problem $$ u''(t)+\lambda a(t)f(u(t)) = 0, \;\;\;t\in(0,1)$$ $$u(0)=0,\;\;\;\; \alpha u(\eta)=u(1),$$ where $0<\eta<1$ and $0<\alpha <\frac{1}{\eta}.$