Abstract
In this work, we consider the following p(x)-Laplacian equation in
where f, V and p(x) are periodic in . 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.
Acknowledgements
The authors would like to express their gratefulness to the referees for useful comments.
Notes
No potential conflict of interest was reported by the authors.