Multiple positive solutions for a critical quasilinear elliptic system

The existence of catΩ(Ω)catΩ(Ω) positive solutions for the pp-Laplacian system with convex and Sobolev critical nonlinearities is obtained by some standard variational methods, whose key is to construct homotopies between ΩΩ and levels of the functional Jλ,μJλ,μ, and some analytical techniques.