The Hénon equation in Orlicz-Sobolev spaces

In this paper, we consider the Hénon problem in the setting of Orlicz-Sobolev spaces: {equation*} {cases} -Δ_g u= |x|^αh( u) in B\\ u>0 in B\\ u= 0 on ∂ B\\ {cases} {equation*}where B is the unit ball in Rⁿ, $g=G'$, $h=H'$ are N-functions and the operator -Δg is the g-Laplacian. We show that the symmetric term |x|^α, for $α>0$, allows to have radial solutions even for supercritical H, generalizing results for the classical Hénon equation. We also show that radial solutions are indeed bounded. Finally, we state a Pohozaev's identity in Orlicz-Sobolev spaces that we apply to get a range in $α$ for which the problem has no bounded solutions.