Solutions For Nonhomgeneous Klein-Gordon-Maxwell Equations With Critical Exponent And Some Related Probleroms

In this paper, we study the existence of solutions for a class of nonhomgeneous Klein-Gordon-Maxwell equations, as follows We consider the solutions of the equations with the following two cases.The first case:when e=1, f(x, u)=|u|2*-1，that isBy using variational methods including Mountain Pass Theorem, we prove the exis-tence of solutions for the equation.The second case:considering when m2-ω2=v(x) base on the first case, that isBe similar to the case one, by employing the variational methods, we obtain the ex-istence of the solutions for the equation. This thesis consist of three chapters. The first chapter is devoted to discuss the introduction mainly including the research back-ground, research situation, research achievements and symbols instruction. In the sec-ond chapter we discuss and resolve the existence of the solutions for the equation under the first case, the main conclusion is Theorem2.1.1. And we research the existence of the solutions for the equation about the second case in the last chapter, the main result is Theorem3.1.1.