MULTIPLE SOLUTIONS FOR CRITICAL ELLIPTICSYSTEMS VIA PENALIZATION METHOD

摘要

We consider the system 1-3~2Δ_u +W(x)u =Q_u(u,v) + 1/2~*K_u(u,v) in R~N,-ε~2Δυ+V(x)υ = Q_υ(u,υ)+ 1/(2~*)K_υ(u, υ) inR~N,u, υ∈H~1(R~N),u(x),υ(x) >0 for eachx∈R~N,where 2~* =2N/(N —2),N ≥3, ε>0 is a parameter,Wand V are positive potentials, and Q and K are homogeneous function withK having critical growth. We relate the number of solutions to thetopology of the set where W and V attain their minimum values. In theproof, we apply Ljusternik-Schnirelmann theory.