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1999 | 135 | 2 | 191-201
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Eigenvalue problems with indefinite weight

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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 $λ_n → ∞$.
Twórcy
  • Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium, Willem@amm.ucl.ac.be
Bibliografia
  • [1] W. Allegretto, Principal eigenvalues for indefinite-weight elliptic problems in $R^n$, Proc. Amer. Math. Soc. 116 (1992), 701-706.
  • [2] W. Allegretto and Y. X. Huang, Eigenvalues of the indefinite-weight p-Laplacian in weighted spaces, Funkc. Ekvac. 38 (1995), 233-242.
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  • [10] Y. X. Huang, Eigenvalues of the p-Laplacian in $R^N$ with indefinite weight, Comm. Math. Univ. Carolin. 36 (1995), 519-527.
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  • [19] M. Willem, Analyse Harmonique Réelle, Hermann, Paris, 1995.
  • [20] M. Willem, Minimax Theorems, Birkhäuser, Boston, 1996.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv135i2p191bwm
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