Abstract
This paper is concerned with the existence of solutions for the following class of singular fourth order elliptic equations
{Delta (|x|(p(x))|Delta u|(p(x)-2)Delta u = a(x)u(-gamma(x)) + lambda f (x, u), in 5 Omega,
u = Delta u = 0, on partial derivative Omega
where Omega is a smooth bounded domain in R-N, gamma : (Omega) over bar -> (0,1) be a continuous function, f is an element of C-1((Omega) over bar x R), p : (Omega) over bar -> (1, infinity) and a is a function that is almost everywhere positive in Omega. Using variational techniques combined with the theory of the generalized Lebesgue-Sobolev spaces, we prove the existence at least one nontrivial weak solution.