Three solutions for three-point boundary value problems

In this paper, we study the existence of at least three solutions for the three-point nonlinear boundary value problems u" (t) + a(t) f(u) = 0, 0 < t < 1; u(0) = 0 = u(1) - gamma u(eta), where eta is an element of (0, 1), gamma is an element of [0, 1], a is an element of C([0, 1], (0, infinity)) and f is an element of C(R, R). Without any monotonicity assumptions on the nonlinear term f by using the increasing operator theory and approximation process, we prove that the three-point boundary value problems has at least three solutions. (c) 2005 Elsevier Ltd. All rights reserved.