Multiple positive solutions for nonlinear third-order three-point boundary-value problems

Abstract

This paper concerns the nonlinear third-order three-point boundary-value problem u‴(t) + h(t)ƒ(u(t)) = 0, t ∈ (0, 1), u(0) = u′(0) = 0, u′(1) = αu′(η), where 0 < η < 1 and 1 < α < 1/η. First, we establish the existence of at least three positive solutions by using the well-known Leggett-Williams fixed point theorem. And then, we prove the existence of at least 2m - 1 positive solutions for arbitrary positive integer m.