Multiple solutions for three-point boundary value problem with nonlinear terms depending on the first order derivative

摘要

In this paper, we consider the following second-order three-point boundary value problemu'' (t) + f(t, u(t), u' (t)) = 0, t ε (0, 1),u (0) = 0, u (1) =ξ u (η)where f : [0, 1] x R-2 &RARR; R is continuous, ξ > 0, 0 < η < such that ξ n < 1. We give conditions on f and two pairs of lower and upper solutions to ensure the existence of at least three solutions of the given problem. Our method is based upon Leray-Schauder degree theory. The emphasis here is that f depends on the first derivative. Our results extend some results in the references.