Application Of Perturbation Methods In Quasilinear Schr(o|")dinger Equations With Critical Exponent

In this paper, we study a class of generalized quasilinear Schrodinger equations of the form-div(g2(u)â–½u)+g(u)g’(u)|â–½u|2+V(x)u=h(u),x∈RN, where N≥3, g(s):Râ†'R+ is a C1 nondecreasing function with respect to|s|, the potential V(x):RNâ†'R is a nonnegative continuous function and the nonlinearity h being pure power function with critical exponent. By working with a perturbation approach and Mountain Pass Lemma, we prove that the problem above has a positive ground state solution. The main work of this paper is to use perturbation methods generalizing the result in Liu et al. [27] to more general quasilinear problem.