About The Research Of The Solutions Of Two Classes Of Nonlinear Equations

Along with science’s and technology’s development, various non-linear problem has aroused people’s widespread interest day by day, because it can well explain various the natural phenomenon. So, the mathematical world and the natural science world attach importance to the nonlinear functional analysis. They have obtained some new results for the nonlinear functional analysis and its applications. The existence of solutions as well as multiplicity, geometric property for a class of Schrodinger equation is also the hot spot which has been discussed in recent years.In this paper, we make use of mountain-pass and fountain theorem to obtain solutions for some expective kinds of Schrodinger equation.The thesis is divided into two chapters according to contents.In Chapter1, under a weaker condition, we study the existence of ground state solution and multiple solutions for the following Schrodinger-Poisson equations: Our results generalize many recent studies.In Chapter2, we obtain solutions of the biharmonic equations,likeMoreover, we study the biharmonic equations with dependence on the gradient, i.e.