Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting
| dc.creator | Mihailescu, Mihai | |
| dc.creator | Radulescu, Vicentiu | |
| dc.date | 2006-06-07 | |
| dc.date.accessioned | 2026-07-07T07:17:01Z | |
| dc.date.available | 2026-07-07T07:17:01Z | |
| dc.description | We study the boundary value problem $-{\rm div}(\log(1+ |\nabla u|^q)|\nabla u|^{p-2}\nabla u)=f(u)$ in $Ω$, $u=0$ on $\partialΩ$, where $Ω$ is a bounded domain in $\RR^N$ with smooth boundary. We distinguish the cases where either $f(u)=-λ|u|^{p-2}u+|u|^{r-2}u$ or $f(u)=λ|u|^{p-2}u-|u|^{r-2}u$, with $p$, $q>1$, $p+q<\min\{N,r\}$, and $r<(Np-N+p)/(N-p)$. In the first case we show the existence of infinitely many weak solutions for any $λ>0$. In the second case we prove the existence of a nontrivial weak solution if $λ$ is sufficiently large. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces. | |
| dc.identifier | https://arxiv.org/abs/math/0606157 | |
| dc.identifier | http://arxiv.org/abs/math/0606157 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113796 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35D05, 35J60, 35J70, 46N20 | |
| dc.title | Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting | |
| dc.type | text |