Existence of ground state solutions for a quasilinear Schroedinger equation with critical growth

摘要

We establish the existence of ground state solutions for a quasilinear Schroedinger equation -Δu + V(x)u - Δ(u~2)u =| u|~(22)~(*-2)u + λ | u|~(p-1) u,in R~N, where N ≥ 3,2~* = (N-2)/(2N), 1 ＜ p ＜ 22~* - 1 and λ ＞ 0 is a parameter. We do not need the subcritical exponent p＞3 which was used by several authors to conclude the existence of solution for the equation above.