Solutions And Properties Of A Class Of Semi-linear Elliptic Equation

About semilinear elliptic equation subject to homogeneous Dirichlet boundary conditions, mathematicians had studied out many good results. In this paper, we study a semilinear elliptic equation subject to homogeneous Dirichlet boundary conditions with three factors firstly. About this equation, on the base of the prior results, by make using of the variational method of Nehari-type and direct, we get some multiplicity result of positive solutions. But some exact solutions results are open. Then we use the bifurcation theorems and spectral analysis to study a special equation of semilinear elliptic equation subject to homogeneous Dirichlet boundary conditions, we can get the exact solutions of this equation, moreover, the solutions structure is studied out. At last, we had studied the solutions of the prior equation by make using of the infinity variational.The paper is organized as follows:In chapter 1, by make using of the variational method of Nehari-type and direct, we get the results about semilinear elliptic equation subject to homogeneous Dirichlet boundary conditions.Chapter 2 are some results about a special equation of semilinear elliptic equation subject to homogeneous Dirichlet boundary conditions, We had used the bifurcation theorems and spectral analysis.At the last chapter, by use of the theorem of infinity bifurcation, we had got the exact solutions and structure of these solutions of the prior equation.