Multiple solutions for a class of nonhomogeneous fourth-order quasilinear equations with nonlinearities

In this paper, we concern with the following nonhomogeneous fourth-order quasilinear equations of the form Delta(2)u - Delta u + V(x)u - k/2 Delta(u)(2)u = f(x, u) + h(x), x is an element of R-N, where Delta(2) := Delta (Delta) is the biharmonic operator, k >= 0, N <= 6, V is an element of C(R-N, R), f is an element of C(R-N x R, R) and h(x) is an element of L-2 (R-N). Under some relaxed assumptions on the nonlinear term f, a new result of multiple nontrivial solutions is obtained via the Ekeland's variational principle and the mountain pass theorem.