Abstract
In this paper we study the existence of multiple solutions for the p(x)-biharmonic operator under Neumann type boundary conditions. By using the variational approach and the Mountain Pass theorem, we obtain the existence of solutions of the problem
{Delta(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
partial derivative/partial derivative v(vertical bar Delta u vertical bar(p(x)-2) Delta u) = m(x)vertical bar u vertical bar(p(x)-2) on partial derivative Omega,
partial derivative u/partial derivative v = 0 on partial derivative Omega,