Sequences of weak solutions for a Navier problem driven by the p(x)-biharmonic operator

We derive the existence of infinitely many solutions for an elliptic problem involving both the p(x)-biharmonic and the p(x)-Laplacian operators under Navier boundary conditions. Our approach is of variational nature and does not require any symmetry of the nonlinearities. Instead, a crucial role is played by suitable test functions in some variable exponent Sobolev space, of which we provide the abstract structure better suited to the framework.