Ground state solution for subcritical Schrödinger-Possion system with irregular potentials

This paper is concerned with the existence of ground state solution for a class of subcritical Schrödinger-Possion systems with irregular potentials. The irregular potentials cause difficulty in recovering the compactness of Palais-Smale sequences by classical method. To conquer this obstacle, with the help of weak ∗ -compactness method, we obtain a new weak ∗ -type splitting lemma, by which we utilize interaction effects among irregular potentials to generate the compactness of (PS) sequences. Some new compactness conditions are introduced to obtain ground state solutions.