On a $p$--Laplace equation with multiple critical nonlinearities
| dc.creator | Filippucci, Roberta | |
| dc.creator | Pucci, Patrizia | |
| dc.creator | Robert, Frédéric | |
| dc.date | 2008-07-06 | |
| dc.date | 2008-09-18 | |
| dc.date.accessioned | 2026-07-07T10:03:24Z | |
| dc.date.available | 2026-07-07T10:03:24Z | |
| dc.description | Using the Mountain--Pass Theorem of Ambrosetti and Rabinowitz we prove that $-Δ_p u-μ|x|^{-p}{u^{p-1}}=|x|^{-s}{u^{\crits-1}}+u^{\crit-1}$ admits a positive weak solution in $\rn$ of class $\dunp\cap C^1(\rn\setminus\{0\})$, whenever $μ<μ_1$, and $μ_1=[(n-p)/p]^p$. The technique is based on the existence of extremals of some Hardy--Sobolev type embeddings of independent interest. We also show that if $u\in\dunp$ is a weak solution in $\rn$ of $-Δ_p u-μ|x|^{-p}{|u|^{p-2}u}=|x|^{-s}{|u|^{\crits-2}u}+|u|^{q-2}u$, then $u\equiv0$ when either $1<q<\crit$, or $q>\crit$ and $u$ is also of class $L^\infty_\text{\scriptsize{loc}}(\rn\setminus\{0\})$. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0807.0913 | |
| dc.identifier | http://arxiv.org/abs/0807.0913 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169278 | |
| dc.subject | Analysis of PDEs | |
| dc.title | On a $p$--Laplace equation with multiple critical nonlinearities | |
| dc.type | text |