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 Ω(?)RN is a bounded smooth domain containing 0,λ∈R,0 ≤ s ≤2,N ≥5,n denotes the unite outward normal vector of(?)Ω,2**=2N/N-4 is the critical Sobolev exponent for the imbedding H02(Ω)→Lp(Ω),and f∈H0-2(Ω).Under suit-able assumptions on the parameters,we prove that the problem(*)possesses at least two weak solutions if ‖f‖H0-2(Ω)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.