POSITIVE SOLUTIONS FOR QUASILINEAR SCHRODINGER EQUATIONS WITH CRITICAL GROWTH AND POTENTIAL VANISHING AT INFINITY

This paper is concerned with the existence of positive solutions for a class of quasilinear Schrodinger equations in R-N with critical growth and potential vanishing at in finity. By using a change of variables, the quasilinear equations are reduced to semilinear one. Since the potential vanish at in finity, the associated functionals are still not well de fined in the usual Sobolev space. So we have to work in the weighted Sobolev spaces, by Hardy-type inequality, then the functionals are well defined in the weighted Sobolev space and satisfy the geometric conditions of the Mountain Pass Theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is classical arguments used by H. Brezis and L. Nirenberg in [13].