抄録
We consider radial solution u(|x|), x ∈ Rn, of a p-Laplace equation with non-linear potential depending also on the space variable x. We assume that the potential is polynomial and it is negative for u small and positive and subcritical for u large.
We prove the existence of radial Ground States under suitable Hypotheses on the potential f(u,|x|). Furthermore we prove the existence of uncountably many radial Singular Ground States; this last result seems to be new even for the spatial independent case and even for p=2.
The proofs combine an energy analysis and the dynamical systems approach developed by Johnson, Pan, Yi and Battelli for the p=2 case.
