Existence and multiplicity results for the nonlinear Schrödinger–Maxwell systems

Abstract

In this paper, we study the nonlinear Schrödinger–Maxwell system where the potential V and the primitive of g are allowed to be sign‐changing, and g is local superlinear. Under some simple assumptions on V,Q and g, we establish some existence criteria to guarantee that the aforementioned system has at least one nontrivial solution or infinitely many nontrivial solutions by using critical point theory. Recent results in the literature are generalized and significantly improved. Copyright © 2015 John Wiley & Sons, Ltd.