The Existence Of Nontrivial Solutions For The Elliptic Equations With Hardy Potential

In this paper we focus mainly on the existence of solutions for a class of elliptic equa-tions with Hardy potential by making use of some conventional theory tools such as compactimbedding theorem,mountain pass lemma,fountain theorem and critical point theory.In chapterⅠ, the historical background, researeh developments, main methods and ae-hievements about elliptic equation are summarized. The main conclusions of this paper aresimply introduced.In chapterⅡ,we study Dirichlet problem solution of an elliptic equation with Hardy poten-tial.We discuss this problem in a new Hilbert space H which is the completion of H02(?).Furthermoreby using the Hardy-Rellich inequality , PS condition and mountain pass theorem we proved thatthere is a nontrivial solution for the problem in the new space H.In chapterⅢ, multiplicity solutions for a quasilinear p-Laplacian equation with Hardy po-tential is discussed. We firstly prove the associated energy functional I(u) satisfy the Cerami'scondition. then we got the existence of multiplicity solutions for the quasilinear p-LaplacianEquation by Foutain theorem .In chapter IV, we discusses a kind of a p-Laplacian equation with Critical exponents andHardy terms, by using Lions'concentrate compactress principle,we prove the associated en-ergy functional Iλ(u) satisfy the PS condition,then we get the nontrivial solution of the problemby mountain pass lemma.In chapter V , we study the multiplicity solutions for a kind of quasilinear p-Laplacian-Like equation with Hardy potential.like chapterⅢ, We prove the associated energy functionalI(u) satisfy the Cerami's condition.then we get the existence of multiplicity solutions by usingthe Foutain theorem .