Existence results for perturbed weighted p(x)-biharmonic problem with Navier boundary conditions

In this paper, we are interested in the study of the following problem with Navier boundary conditions Delta(vertical bar x vertical bar(p(x))vertical bar Delta u vertical bar(p(x)-2) Delta u) = lambda V(x)vertical bar u vertical bar(q(x)-2)u in Omega, u = Delta u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-n, lambda > 0, the potential V is in some generalized Sobolev space, and p, q : Omega -> [1,infinity) are continuous functions. The main tools used here are based on the variational method combined with the Mountain Pass theorem and Ekeland variational principle.