Multiple solutions for nonhomogeneous Schrödinger-Maxwell and Klein-Gordon-Maxwell equations on R3

Abstract

In this paper we study the following nonhomogeneous Schrödinger-Maxwell equations, where f satisfies the Ambrosetti-Rabinowitz type condition. Under appropriate assumptions on V, f and h, the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. Similar results for the nonhomogeneous Klein-Gordon-Maxwell equations, are also obtained when 2 < q < 6. © 2010 Birkhäuser / Springer Basel AG.