A problem involving the \(p\)-Laplacian operator
Using a variational technique we guarantee the existence of a solution to the \emph{resonant Lane-Emden} problem \(-\Delta_p u=\lambda |u|^{q-2}u\), \(u|_{\partial\Omega}=0\) if and only if a solution to \(-\Delta_p u=\lambda |u|^{q-2}u+f\), \(u|_{\partial\Omega}=0\), \(f\in L^{p'}(\Omega)\) (\...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2016-01 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | Using a variational technique we guarantee the existence of a solution to the \emph{resonant Lane-Emden} problem \(-\Delta_p u=\lambda |u|^{q-2}u\), \(u|_{\partial\Omega}=0\) if and only if a solution to \(-\Delta_p u=\lambda |u|^{q-2}u+f\), \(u|_{\partial\Omega}=0\), \(f\in L^{p'}(\Omega)\) (\(p'\) being the conjugate of \(p\)), exists for \(q\in (1,p)\bigcup (p,p^{*})\) under a certain condition for both the cases, i.e., \(1 |
|---|---|
| ISSN: | 2331-8422 |