Positive Solutions for a Nonlinear Three-point Boundary-value Problem

Abstract

We study the existence of positive solutions to the boundary-value problem u'' + α(t)ƒ(u) = 0, t ∈ (0,1) u(0) = 0, αu(ƞ) = u(1), where 0 < ƞ < 1 and 0 < α < 1/ƞ. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.