Multiplicity Solutions For A Class Of Semilinear Schr(?)dinger Equations

In this paper, we study the multiplicity solutions for a class of semilinear Schrodinger equations. We mainly carry out the reduction and use the number of the bumps of the solutions, as the parameter to construct the approximate solutions for the semilinear Schrodinger equation. Then, we verify that the approximate solutions are the critical points of the corresponding function and prove the existence of multiplicity non-radical positive solutions.The main work in this paper is as follows:1. Sketching the background, the present situation and the main results of the related problems at home and abroad:2. Giving some preliminary knowledge, including some frequently-used inequalities and basic theorems. Sobolve space and embedding theorem;3. Proving the main results of this paper. Firstly, we use the number of the bumps of the solutions, as the parameter to construct the approximate solutions for the equation and give the corresponding function. Then, we define a new function and prove the existence of its critical points. Finally, we give the energy expansion for the approximate solutions and prove the existence of multiplicity non-radical positive solutions.