Infinitely many solutions for the Hénon equation with critical exponent in non-convex domains.

We consider the Neumann problem for the Hénon equation -Δu+u=|x|2αu(N+2)/(N-2), u>0, in Ω, ∂u/∂n=0 on ∂Ω, (0.1) where Ω⊂RN,N≥3 is a smooth and bounded domain, α>0 and n denotes the outward unit normal vector of ∂Ω. We show that problem (0.1) has infinitely many positive solutions, whose energy can be made arbitrarily large in some (partially symmetric) non-convex domains Ω. This seems to be a new phenomenon for the Hénon equation in bounded domains. [ABSTRACT FROM AUTHOR]