A note on the implicit function theorem for quasi-linear eigenvalue problems

We consider the quasi-linear eigenvalue problem \(-\Delta_p u = \lambda g(u)\) subject to Dirichlet boundary conditions on a bounded open set \(\Omega\), where \(g\) is a locally Lipschitz continuous functions. Imposing no further conditions on \(\Omega\) or \(g\) we show that for small \(\lambda\)...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Nittka, Robin
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.09.2011
Subjects
Boundary conditions
Continuity (mathematics)
Dirichlet problem
Eigenvalues
Mathematics - Analysis of PDEs
Online AccessGet full text

Cover

More Information
Summary:We consider the quasi-linear eigenvalue problem \(-\Delta_p u = \lambda g(u)\) subject to Dirichlet boundary conditions on a bounded open set \(\Omega\), where \(g\) is a locally Lipschitz continuous functions. Imposing no further conditions on \(\Omega\) or \(g\) we show that for small \(\lambda\) the problem has a bounded solution which is unique in the class of all small solutions. Moreover, this curve of solutions depends continuously on \(\lambda\).
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1109.5089