EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR KLEIN-GORDON-MAXWELL SYSTEM WITH A PARAMETER

Abstract

. This paper is concerned with the following Klein-Gordon-Maxwell system: where ω > 0 is a constant and λ is the parameter. Under some suitable assumptions on V ( x ) and f ( x,u ), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition. 35B38.