The Existence Of Two Weak Solutions Of Biharmonic Equations Involving A Hardy Singular Term And The Sobolev Critical Exponent And Non-homogeneous Term

In this paper,we use variational method to study the following nonlinear bihar-monic elliptic problemsinvolving a Hardy singular term and the Sobolev critical exponent and non-homogeneous term,where ?(?)RN is a bounded smooth domain containing 0,??R,0 ? s ?2,N ?5,n denotes the unite outward normal vector of(?)?,2**=2N/N-4 is the critical Sobolev exponent for the imbedding H02(?)?Lp(?),and f?H0-2(?).Under suit-able assumptions on the parameters,we prove that the problem(*)possesses at least two weak solutions if ?f?H0-2(?)is suitablly small.Our main results generalizes the main result of G.Tarantello?Ann.Inst.Henri Poincare?281-304(1992)from non-linear harmonic equations to nonlinear biharmonic equations and the main result of Yinbin Deng,Gengsheng Wang?Proc.Royal Soc.Edinburgh?925-946(1999)about biharmonic equation to the case involving a Hardy singular term.