The Existence Of Two Solutions For Quasilinear Elliptic Equation With Hardy Singular Term

In this paper, we used variational method to consider the following quasilinear elliptic equation involving Hardy singular term and Sobolev critical exponent:where N ? 3, N > p ? 2, 0? ?<?=(N-p/p)p,p*=Np/N-p is Sobolev critical exponent and g(x) ? 0, g(x)(?)0. We show that if g(x)?Lp*/p*-1(RN) then the above problem has at least two nontrivial solutions. One solution is obtained by local extremum method and the other is obtained by using mountain pass lemma.