We consider radial solution u(vertical bar x vertical bar), x is an element of R-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, vertical bar x vertical bar). 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.
Ground states and singular ground states for quasilinear elliptic equations in the subcritical case
FRANCA, Matteo
2005-01-01
Abstract
We consider radial solution u(vertical bar x vertical bar), x is an element of R-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, vertical bar x vertical bar). 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
