Ground state solutions andmultiple solutions for a p(x)-Laplacian equation in RN with periodic data

In this work, we consider the following p(x)-Laplacian equation in R-N {- div(|Delta u|(p(x))-2(del u)) + V(x)|u| (p(x)-2)u = f (x, u), in R-N u is an element of W-1,W- p(x)(R-N), where f, V and p( x) are periodic in x(1), x(2),..., x(N). Under some appropriate assumptions, we prove the existence of the ground state solutions via the generalized Nehari method due to Szulkin and Weth. Moreover, if f is odd in u, infinitely many pairs of geometrically distinct solutions are given. To the best of our knowledge, our results are new even in the constant exponent case.