Nonlinear eigenvalue problems in Sobolev spaces with variable exponent
| dc.creator | Dinu, Teodora Liliana | |
| dc.date | 2005-11-08 | |
| dc.date.accessioned | 2026-07-07T06:50:57Z | |
| dc.date.available | 2026-07-07T06:50:57Z | |
| dc.description | We study the boundary value problem $-{\rm div}((|\nabla u|^{p\_1(x) -2}+|\nabla u|^{p\_2(x)-2})\nabla u)=f(x,u)$ in $Ω$, $u=0$ on $\partialΩ$, where $Ω$ is a smooth bounded domain in $\RR^N$. We focus on the cases when $f\_\pm (x,u)=\pm(-λ|u|^{m(x)-2}u+|u|^{q(x)-2}u)$, where $m(x):=\max\{p\_1(x),p\_2(x)\} < q(x) < \frac{N\cdot m(x)}{N-m(x)}$ for any $x\in\barΩ$. In the first case we show the existence of infinitely many weak solutions for any $λ>0$. In the second case we prove that if $λ$ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a $\ZZ\_2$-symmetric version for even functionals of the Mountain Pass Lemma and some adequate variational methods. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0511193 | |
| dc.identifier | http://arxiv.org/abs/math/0511193 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104829 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35D05, 35J60, 35J70, 58E05, 68T40, 76A02 | |
| dc.title | Nonlinear eigenvalue problems in Sobolev spaces with variable exponent | |
| dc.type | text |