Full metadata record
| DC pole | Hodnota | Jazyk |
|---|---|---|
| dc.contributor.author | Audoux, Benjamin | |
| dc.contributor.author | Bobkov, Vladimír | |
| dc.contributor.author | Parini, Enea | |
| dc.date.accessioned | 2018-10-21T10:00:13Z | |
| dc.date.available | 2018-10-21T10:00:13Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 1230-3429 | |
| dc.identifier.uri | http://hdl.handle.net/11025/30447 | |
| dc.format | 18 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | en | en |
| dc.publisher | Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies | en |
| dc.rights | Plný text není přístupný. | cs |
| dc.rights | © Nicolaus Copernicus University in Torun, Juliusz Schauder Centre for Nonlinear Studies | en |
| dc.title | On multiplicity of eigenvalues and symmetry of eigenfunctions of the p--Laplacian | en |
| dc.type | článek | cs |
| dc.type | article | en |
| dc.rights.access | closedAccess | en |
| dc.type.version | publishedVersion | en |
| dc.description.abstract-translated | We investigate multiplicity and symmetry properties of higher eigenvalues and eigenfunctions of the $p$-Laplacian under homogeneous Dirichlet boundary conditions on certain symmetric domains $\Omega \subset \R^N$. By means of topological arguments, we show how symmetries of $\Omega$ help to construct subsets of $W_0^{1,p}(\Omega)$ with suitably high Krasnosel'ski\u{\i} genus. In particular, if $\Omega$ is a ball $B \subset \mathbb{R}^N$, we obtain the following chain of inequalities: $$ \lambda_2(p;B) \leq \dots \leq \lambda_{N+1}(p;B) \leq \lambda_\ominus(p;B). $$ Here $\lambda_i(p;B)$ are variational eigenvalues of the $p$-Laplacian on $B$, and $\lambda_\ominus(p;B)$ is the eigenvalue which has an associated eigenfunction whose nodal set is an equatorial section of $B$. If $\lambda_2(p;B)=\lambda_\ominus(p;B)$, as it holds true for $p=2$, the result implies that the multiplicity of the second eigenvalue is at least $N$. In the case $N=2$, we can deduce that any third eigenfunction of the $p$-Laplacian on a disc is nonradial. The case of other symmetric domains and the limit cases $p=1$, $p=\infty$ are also considered. | en |
| dc.subject.translated | p-Laplacian | en |
| dc.subject.translated | nonlinear eigenvalues | en |
| dc.subject.translated | Krasnoselskii genus | en |
| dc.subject.translated | symmetry | en |
| dc.subject.translated | multiplicity | en |
| dc.subject.translated | degree of map. | en |
| dc.identifier.doi | 10.12775/TMNA.2017.055 | |
| dc.type.status | Peer-reviewed | en |
| dc.identifier.document-number | 441425700011 | |
| dc.identifier.obd | 43922716 | |
| dc.project.ID | LO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost | cs |
| Vyskytuje se v kolekcích: | Články / Articles (KMA) OBD | |
Soubory připojené k záznamu:
| Soubor | Velikost | Formát | |
|---|---|---|---|
| Audoux-Bobkov-Parini_final_pub-2018.pdf | 544,48 kB | Adobe PDF | Zobrazit/otevřít Vyžádat kopii |
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