Multiple positive solutions for nonlinear three-point boundary value problems on time scales

Abstract

In this paper, we consider the nonlinear second-order three-point boundary value problem u ? ? (t) + h (t) f (t, u (t)) = 0, t ? [t 1 , t 3 ] ? T,u ? (t 3 ) = 0, ? u (t 1 ) - ß u ? (t 1 ) = u ? (t 2 ), where T is a time scale, 0 ? t 1 < t 2 < t 3 , ? > 0 and ß ? 0 are given constants. By using fixed-point theorems in cones, some new results are obtained for the existence of at least one,two and three positive solutions of the above problem. © 2007 Elsevier Ltd. All rights reserved.