The Numbers of Positive Solutions by the Lusternik-Schnirelmann Category for a Quasilinear Elliptic System Critical with Hardy Terms

Abstract

In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains. By employing the technique introduced by Benci and Cerami (1991), we obtain at least $\mathrm{c}\mathrm{a}\mathrm{t}(\mathrm{\Omega })+\mathrm{1}$ distinct positive solutions.