Two Types of Solutions to a Class of (p,q)‎-Laplacian Systems with Critical Sobolev Exponents in RN

Abstract EN

We focus on the following elliptic system with critical Sobolev exponents: -div∇up-2∇u+m(x)up-2u=λup⁎-2u+(1/η)Gu(u,v), x∈RN; -div∇vq-2∇v+n(x)vq-2v=μvq⁎-2v+(1/η)Gv(u,v), x∈RN; u(x)>0,v(x)>0, x∈RN, where μ,λ>0,1

Conditions on potential functions m(x),n(x) lead to no compact embedding.

Relying on concentration-compactness principle, mountain pass lemma, and genus theory, the existence of solutions to the elliptic system with η∈(q,p⁎) or η∈(1,p) will be established.