Eigenvalue problems with indefinite weight

• Autorzy: Andrzej Szulkin , Michel Willem
• Języki publikacji: EN

Abstrakty

EN

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 $λ_n → ∞$.

Słowa kluczowe

EN

eigenvalue problem; Laplacian; p-Laplacian; indefinite weight

Kategorie tematyczne

• 35J20: Variational methods for second-order elliptic equations
• 35J70: Degenerate elliptic equations
• 35P05: General topics in linear spectral theory
• 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 135
• Numer: 2
• Strony: 191-201

Daty

wydano

1999

poprawiono

1998-11-26

otrzymano

1999-06-04

Twórcy

autor

Andrzej Szulkin

• Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden,

autor

Michel Willem

• Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium,

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