Existence of solutions for perturbed fourth order elliptic equations with variable exponents

Using variational methods, we study the existence and multiplicity of solutions for a class of fourth order elliptic equations of the form {Delta(2)(p(x))u - M (integral(Omega)1/p(x)vertical bar del u vertical bar(p(x))dx) Delta(p(x))u = f(x, u) in Omega, u = Delta u = 0 an partial derivative Omega, where Omega subset of R-N, N >= 3, is a smooth bounded domain, Delta(2)(p(x))u = Delta(vertical bar Delta u vertical bar(p(x)-2) Delta u) is the operator of fourth order called the p(x)-biharmonic operator, Delta(p(x)) u = div (vertical bar del u vertical bar(p(x)-2)del u) is the p(x)-Laplacian, p : (Omega) over bar -> R is a log-Holder continuous function, M : [0, +infinity) -> R and f : Omega x R -> R are two continuous functions satisfying some certain conditions.