Existence of a positive solution for some quasilinear elliptic equations in [formula omitted

Abstract

We study the existence of a positive solution of the following quasilinear elliptic equations in RN:−Δpu=g(u),u∈W1,p(RN), where N≥2, 1<p≤N and Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator. We assume that g(s) satisfies Berestycki-Lions type condition. We give a new concentration compactness type result for a Palais-Smale sequence with an additional property related to Pohozaev identity. Keys of our proof are Tartar's inequality and Brezis-Lieb Lemma.