Ground states and singular ground states for quasilinear elliptic equations in the subcritical case

We consider radial solution $u(|x|)$, $x in RR^n$, 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 a new dynamical systems method.