Eigenvalues of the p -Laplacian in 𝐑 N with indefinite weight

Yin Xi Huang

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 3, page 519-527
  • ISSN: 0010-2628

Abstract

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We consider the nonlinear eigenvalue problem - div ( | ∇ u | p - 2 ∇ u ) = λ g ( x ) | u | p - 2 u in 𝐑 N with p > 1 . A condition on indefinite weight function g is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in W 1 , p ( 𝐑 N ) . A nonexistence result is also given for the case p ≥ N .

How to cite

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Huang, Yin Xi. "Eigenvalues of the $p$-Laplacian in ${\mathbf {R}}^N$ with indefinite weight." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 519-527. <http://eudml.org/doc/247770>.

@article{Huang1995,
abstract = {We consider the nonlinear eigenvalue problem \[ -\operatorname\{div\}(|\{\nabla \} u|^\{p-2\}\{\nabla \} u)=\lambda g(x)|u|^\{p-2\}u \] in $\mathbf \{R\}^N$ with $p>1$. A condition on indefinite weight function $g$ is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in $\{W^\{1, p\}(\mathbf \{R\}^N)\}$. A nonexistence result is also given for the case $p\ge N$.},
author = {Huang, Yin Xi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {eigenvalue; the $p$-Laplacian; indefinite weight; $\mathbf \{R\}^N$; -Laplacian; indefinite weight; nonexistence of positive solutions; existence; Lyusternik-Schnirelmann theory},
language = {eng},
number = {3},
pages = {519-527},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Eigenvalues of the $p$-Laplacian in $\{\mathbf \{R\}\}^N$ with indefinite weight},
url = {http://eudml.org/doc/247770},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Huang, Yin Xi
TI - Eigenvalues of the $p$-Laplacian in ${\mathbf {R}}^N$ with indefinite weight
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 519
EP - 527
AB - We consider the nonlinear eigenvalue problem \[ -\operatorname{div}(|{\nabla } u|^{p-2}{\nabla } u)=\lambda g(x)|u|^{p-2}u \] in $\mathbf {R}^N$ with $p>1$. A condition on indefinite weight function $g$ is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in ${W^{1, p}(\mathbf {R}^N)}$. A nonexistence result is also given for the case $p\ge N$.
LA - eng
KW - eigenvalue; the $p$-Laplacian; indefinite weight; $\mathbf {R}^N$; -Laplacian; indefinite weight; nonexistence of positive solutions; existence; Lyusternik-Schnirelmann theory
UR - http://eudml.org/doc/247770
ER -

References

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