Existence Of Exceptional Solutions For Two Schrodinger - Maxwell Equations

In modern society, the science and technology develop quickly and all kinds of nonlinear problems arise in physics,applied mathematics,cybernetics and other scienti?c ?elds.There problems draw people’s attention. the nonlinear functional analysis which is a powerful tool to deal with these problems has become one important research directions in modern mathematics.The nonlinear functional analysis has the profound theory and the widespread application and takes the nonlinear problems as a background to establish some general theories and methods to handle nonlinear problems.In this paper,we use the symmetric mountain pass theorem to study the existence of multiple solutions for two different kinds of Schr¨odinger-Maxwell equations.The thesis is divided into three sections according to contents.Chapter 1 We introduce some fundamental knowledge and source of theory.Chapter 2 We consider multiple solutions for the following superlinear Schr¨odingerMaxwell equation with nodal potential:Chapter 3 we consider multiple solutions for the following sublinear Schr¨odingerMaxwell equation:...