The Existence Of Solution And Multiple Solutions For Two Elliptic Partial Differential Equations

In this thesis, by using some approach in variational methods, such as minimax principle and moutain-pass lemma, we study the existence and multiplity of solutions to two elliptic partial differential equations.In chapter one, we review some backgroud of problems in the thesis.In chapter two, by using the Limit Index, we prove theorems applying to get multiple critical values of some strongly indefinite nonsmooth functionals, and then we apply it to a system of equations involving the p-Laplacian.WhereΩis a bounded domain, the functional corresponding to the equations (S) may be nonsmooth. We get multiple weak solutions of (S).In chapter three, we consider the existence of solution for a quasilinear Schrodinger equation.By using of the mountain-pass lemma and a dual approach, we obtain a solution of (3.1.1).