Eigenvalue problems for the p-Laplacian

We study nonlinear eigenvalue problems for the p -Laplace operator subject to different kinds of boundary conditions on a bounded domain. Using the Ljusternik–Schnirelman principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues. We prove the simplicity and isolation of...

Full description

Saved in:
Bibliographic Details
Published inNonlinear analysis Vol. 64; no. 5; pp. 1057 - 1099
Main Author LE, An
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.03.2006
Elsevier
Subjects
Exact sciences and technology
Ljusternik–Schnirelman principle
Mathematical analysis
Mathematics
Nonlinear eigenvalue problems
p-Laplacian
Partial differential equations
Sciences and techniques of general use
Variational methods
p-Laplacian
Variational methods
35J60
Nonlinear eigenvalue problems
35B45
35J70
Ljusternik–Schnirelman principle
P laplacian
Nonlinear analysis
35J70 Nonlinear eigenvalue problems
Nonlinear problems
Eigenvalue problem
Ljusternik Schnirelman principle
Ljusternik-Schnirelman principle
Online AccessGet full text

Cover

More Information
Summary:We study nonlinear eigenvalue problems for the p -Laplace operator subject to different kinds of boundary conditions on a bounded domain. Using the Ljusternik–Schnirelman principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues. We prove the simplicity and isolation of the principal eigenvalue and give a characterization for the second eigenvalue.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2005.05.056