POSITIVE GROUND STATE SOLUTIONS FOR A QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL EXPONENT

In this paper, we study the following quasilinear elliptic equation with critical Sobolev exponent: -Delta u + V(x)u - [Delta(1 + u(2))(1/2)]u/2(1+u(2))(1/2) = |u|(2*-2)u + |u|(p-2)u, x is an element of R-N, which models the self-channeling of a high-power ultra short laser in matter, where N >= 3, 2 < p < 2* - 2N/N-2 and V(x) is a given positive potential. Combining the change of variables and an abstract result developed by Jeanjean in [14], we obtain the existence of positive ground state solutions for the given problem.