A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces
| dc.creator | Mihailescu, Mihai | |
| dc.creator | Radulescu, Vicentiu | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:41:02Z | |
| dc.date.available | 2026-07-07T08:41:02Z | |
| dc.description | We study the nonlinear eigenvalue problem $-{\rm div}(a(|\nabla u|)\nabla u)=λ|u|^{q(x)-2}u$ in $Ω$, $u=0$ on $\partialΩ$, where $Ω$ is a bounded open set in $\RR^N$ with smooth boundary, $q$ is a continuous function, and $a$ is a nonhomogeneous potential. We establish sufficient conditions on $a$ and $q$ such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational arguments. The abstract results of this paper are illustrated by the cases $a(t)=t^{p-2}\log (1+t^r)$ and $a(t)= t^{p-2} [\log (1+t)]^{-1}$. | |
| dc.identifier | https://arxiv.org/abs/0711.0904 | |
| dc.identifier | http://arxiv.org/abs/0711.0904 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141555 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35D05, 35J60, 35J70, 58E05, 68T40, 76A02 | |
| dc.title | A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces | |
| dc.type | text |