Eigenvalue problems with indefinite weight

Andrzej Szulkin; Michel Willem

Studia Mathematica (1999)

  • Volume: 135, Issue: 2, page 191-201
  • ISSN: 0039-3223

Abstract

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We consider the linear eigenvalue problem -Δu = λV(x)u, u ∈ D 0 1 , 2 ( Ω ) , and its nonlinear generalization - Δ p u = λ V ( x ) | u | p - 2 u , u ∈ D 0 1 , p ( Ω ) . The set Ω need not be bounded, in particular, Ω = ℝ N is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues λ n → ∞ .

How to cite

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Szulkin, Andrzej, and Willem, Michel. "Eigenvalue problems with indefinite weight." Studia Mathematica 135.2 (1999): 191-201. <http://eudml.org/doc/216650>.

@article{Szulkin1999,
abstract = {We consider the linear eigenvalue problem -Δu = λV(x)u, $u ∈ D^\{1,2\}_0(Ω)$, and its nonlinear generalization $-Δ_\{p\}u = λV(x)|u|^\{p-2\}u$, $u ∈ D^\{1,p\}_0(Ω)$. The set Ω need not be bounded, in particular, $Ω = ℝ^N$ is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues $λ_n → ∞$.},
author = {Szulkin, Andrzej, Willem, Michel},
journal = {Studia Mathematica},
keywords = {eigenvalue problem; Laplacian; p-Laplacian; indefinite weight; -Laplacian},
language = {eng},
number = {2},
pages = {191-201},
title = {Eigenvalue problems with indefinite weight},
url = {http://eudml.org/doc/216650},
volume = {135},
year = {1999},
}

TY - JOUR
AU - Szulkin, Andrzej
AU - Willem, Michel
TI - Eigenvalue problems with indefinite weight
JO - Studia Mathematica
PY - 1999
VL - 135
IS - 2
SP - 191
EP - 201
AB - We consider the linear eigenvalue problem -Δu = λV(x)u, $u ∈ D^{1,2}_0(Ω)$, and its nonlinear generalization $-Δ_{p}u = λV(x)|u|^{p-2}u$, $u ∈ D^{1,p}_0(Ω)$. The set Ω need not be bounded, in particular, $Ω = ℝ^N$ is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues $λ_n → ∞$.
LA - eng
KW - eigenvalue problem; Laplacian; p-Laplacian; indefinite weight; -Laplacian
UR - http://eudml.org/doc/216650
ER -

References

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