A Solution 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 of solutions for two kinds of elliptic partial differential equations.First, we think of a solution for a class of p-Laplacian equation: whereΩis a bounded domain in RN with smooth boundaryЭΩ, pλ1 on a set of positive measure. And discuss separately a nontrivial positive solution and a nontrivial solution for (1.2.2). The thesis consists of four chapters.In chapter one, we review some background and resuls above mentioned, some basic problems we considered.In chapter two, we recall some basic knowledge about critical theory, and some basic lemmas which are needed in the following chapters.In chapter three, we discuss a nontrivial solution for (1.2.1), using concentration-compactness lemma and mountai-pass lemma.In chapter four, we discuss separately a nontrivial positive solution and a non-trivial solution for (1.2.2), using minimization lemma.