Multiple solutions for nonhomogeneous Schrodinger-Maxwell and Klein- Gordon-Maxwell equations on R 3

In this paper we study the following nonhomogeneous Schrodinger-Maxwell equations {-Delta u + V(x)u + phi u = f(x, u) + h(x), in R-3, -Delta phi = u(2), in R-3, 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 {-Delta u + [m(2) - (omega + phi)(2)]u = vertical bar mu vertical bar(q-2)u + h(x), in R-3, {-Delta phi + phi mu(2) = -omega mu(2), in R-3, are also obtained when 2 < q < 6.