On a perturbed p(x)p(x)-Laplacian problem in bounded and unbounded domains

In this paper we investigate the existence of multiple solutions for a quasilinear elliptic equation involving the p(x)p(x)-Laplacian in which the nonlinearity depends on three real parameters. The solutions we look for are defined in a domain of RnRn which we allow to be possibly unbounded. Our approach relies upon variational arguments.