Existence of solution for a class of quasilinear Schrödinger equation in [formula omitted] with zero-mass

Abstract

In this paper we investigate the existence of solutions for the following quasilinear Schrödinger problem with zero-mass:{−Δu−kΔ(u2)u=h(x)uqinRN,u≥0,u∈D1,2(RN)∩L∞(RN), where k>0, 0≤q<2.2⁎−1 and 2⁎=2N/(N−2);N≥3 is the critical Sobolev exponent and h∈Lloc∞(RN) is a function that can change sign. To establish existence results we used the variational method. More precisely, we used a change of variables combined with the Ekeland Variational Principle, Mountain Pass Theorem, careful estimates on energy functionals and an argument of passing to the limit.