On multiple solutions of a singular quasilinear equation on unbounded domain

Variational methods are used to prove existence and multiplicity of solutions for the following quasilinear partial differential equation −Δpu = α|x|−s |u|p∗(s)−2u + βk(x)× |u|r−2u in Ω, where 0 s p, Ω ⊂ RN may be unbounded. In particular, Ω = RN is permitted.  2002 Elsevier Science (USA). All rights reserved