Multiple solutions to fourth-order boundary value problems

In this paper, we study the existence and multiplicity of solutions to the fourth-order boundary value problem u((4))(t) + beta u ''(t) - alpha u(t) = f(t, u(t)) for all t is an element of vertical bar 0, 1 vertical bar subject to Dirichlet boundary value condition, where f is an element of C-1(vertical bar 0, 1 vertical bar x R-1, R-1), alpha, beta is an element of R-1. By using the critical point theory and the infinite dimensional Morse theory, we establish some conditions on f which are able to guarantee that this boundary value problem has at least one nontrivial, two nontrivial, m distinct pairs of solutions, and infinitely many solutions, respectively. Our results improve some recent works. (C) 2008 Elsevier Ltd. All rights reserved.