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.
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