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EnglishWe 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.
| Titolo: | Ground states and singular ground states for quasilinear elliptic equations in the subcritical case | |
| Autori: | ||
| Data di pubblicazione: | 2005 | |
| Rivista: | ||
| 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. | |
| Handle: | http://hdl.handle.net/11566/39316 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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