Solution For A Quasilinear Schrodinger Equation Involving Hardy Potential

In this paper,we consider the following quasilinear Schrodinger equation with Hardy potential where Ω is a bounded domain with zero point,the potential V(x):Ω→R~+ is a continuous function,k>0,0≤μ≤μ=((N-2_/2)/2 is the best constant of Hardy inequality.When 4<p<2 · 2*,we prove that the equation has nontrivial solutions by Mountain Pass Lemma,when p≥2·2*,we prove that the equation has no nontrivial solution by the Pohozaev identity.