EXISTENCE OF SOLUTIONS FOR FOURTH-ORDER PDES WITH VARIABLE EXPONENTS

In this article, we study the following problem with Navier boundary conditions Delta(2)(p)((x))u = lambda|u|(p( x)) (2)u + f(x, u) in Omega, u = Delta u = 0 on partial derivative Omega. Where Omega is a bounded domain in R-N with smooth boundary partial derivative Omega, N >= 1, Delta(2)(p)((x))u := Delta(|Delta u|(p(x)-2)Delta u), is the p(x)-biharmonic operator, lambda <= 0, p is a continuous function on Omega with inf(x is an element of Omega)p(x) > 1 and f : Omega x R -> R is a Caratheodory function. Using the Mountain Pass Theorem, we establish the existence of at least one solution of this problem. Especially, the existence of infinite many solutions is obtained.