On The Existence Of The Solution Of Nonhomogeneous Biharmonic Elliptics Equations Involving Critical Sobolev Exponent

In this paper we consider the existence of the following critical growth biharmonic elliptic equation where Ω(?)RN(N>4)is a bounded smooth domain,h∈H-2(Ω),2*=N-4/2N is the critical Sobolev exponent for the embedding H2(RN)â†'L2*(RN).Define the functional and Nehari manifbld M={μ∈H02(Ω):(J’(μ),μ)=0). We investigate Ekeland variational principle and Nehari manifold to proof the following theorem. Theorem1.1Let h≠0satisfies where CN=N-4/8(N+4/N-4)8/N+4then is achieved at a point μ0∈M which is a critical point for J.Moreover if h satisfies the more restrictive assumption then μ0is a local minimum for JThis paper includes three chapters.In chapter1,we present a simple research summary of the following critical growth biharmonic elliptic equation,list the main theorems in this paper.In chapter2,we list some preknowledges and lemmas.In chapter3,we present the process proved of theorems1.1.