High energy solutions to p(x)-Laplacian equations of schrodinger type

In this article, we study nonlinear Schrodinger type equations in R^N under the framework of variable exponent spaces. We proposed new assumptions on the nonlinear term to yield bounded Palais-Smale sequences and then prove that the special sequences we found converge to critical points respectively. The main arguments are based on the geometry supplied by Fountain Theorem. Consequently, we showed that the equation under investigation admits a sequence of weak solutions with high energies