Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions

In this work we will study the eigenvalues for a fourth order elliptic equation with p(x)-growth conditions Delta(2)(p(x))u = lambda vertical bar u vertical bar(p(x)-2) u, under Neumann boundary conditions, where p(x) is a continuous function defined on the bounded d(7.) main with p(x) > 1. Through the Ljusternik-Schnirelernan theory on C-1-manifold, we prove the existence of infinitely many eigenvalue sequences and sup Lambda = +infinity where Lambda is the set of all eigenvalues.