Existence of three solutions for a doubly eigenvalue fourth-order boundary value problem

Abstract

In this paper we consider the existence of at least three solutions for the Dirichlet problem u(iv) + alpha u '' + beta u - lambda f(x, u) + mu g(x, u), x is an element of (0, 1) u(0) = u(1) = 0, u ''(0) = u ''(1) = 0 where alpha, beta are real constants, f, g : [0, 1] x R -> R are L(2)-Caratheodory functions and lambda, mu > 0. The approach is based on variational methods and critical points.