On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent
| 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 consider the nonlinear eigenvalue problem $-{\rm div}(|\nabla u|^{p(x)-2}\nabla u)=λ|u|^{q(x)-2}u$ in $Ω$, $u=0$ on $\partialΩ$, where $Ω$ is a bounded open set in $\RR^N$ with smooth boundary and $p$, $q$ are continuous functions on $\barΩ$ such that $1<\inf\_Ωq< \inf\_Ωp<\sup\_Ωq$, $\sup\_Ωp<N$, and $q(x)<Np(x)/(N-p(x))$ for all $x\in\barΩ$. The main result of this paper establishes that any $λ>0$ sufficiently small is an eigenvalue of the above nonhomogeneous quasilinear problem. The proof relies on simple variational arguments based on Ekeland's variational principle. | |
| dc.identifier | https://arxiv.org/abs/math/0606156 | |
| dc.identifier | http://arxiv.org/abs/math/0606156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113795 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35D05, 35J60, 35J70, 58E05, 68T40, 76A02 | |
| dc.title | On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent | |
| dc.type | text |