Existence of positive solutions for a class of p-Laplacian type generalized quasilinear Schrodinger equations with critical growth and potential vanishing at infinity

In this paper, we study the existence of positive solutions for the following generalized quasilinear Schrodinger equation- div(gp(u) |V u |p-2V u) + gp-1(u)g '(u) | V u |p + V(x) | u |p-2u = K(x)f(u) + Q(x)g(u)|G(u) |p*-2G(u), x E RN,where N > 3, 1 < p < N, p* = N p N-p , g E C1(R,R+), V(x) and K(x) are positive con-tinuous functions and G(u) = f0u g(t)dt. By using a change of variable, we obtain the existence of positive solutions for this problem by using the Mountain Pass Theorem. Our results generalize some existing results.