Existence Of Solutions For Two Classes Of Elliptic Equations

In this thesis, we study the existence of solutions to two class of elliptic equations or elliptic systems by using variational methods, such as mountain pass lemma, fountain theorem.In the first chapter, we review some background of problems related to our thesis. In the second chapter, we introduce some basic knowledge in this thesis and give some notations, definitions, and lemmas.In chapter three and chapter four, we study a class of degenerate elliptic equations We obtain the existence of solutions in different hypotheses.In chapter five and chapter six, we study the following elliptic equation with critical Hardy-Sobolev exponent When μ=0, s=0,we get infinitely many solutions. When p=2,we obtain a positive solution.