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Positive Eigenfunctions of a Schrödinger Operator

Stuart, C. A. ; Zhou, Huan-Song

In: Journal of the London Mathematical Society, 2005, vol. 72, no. 2, p. 429-441

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    Titre
    • Positive Eigenfunctions of a Schrödinger Operator
    Auteur
    • Stuart, C. A.. IACS-FSB, Section de Mathématiques, École Polytechnique Fédérale de Lausanne CH-1015 Lausanne, Switzerland
    • Zhou, Huan-Song. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences PO Box 71010, Wuhan 430071, China
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of the London Mathematical Society, 2005, vol. 72, no. 2, p. 429-441. Oxford University Press
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:303701
    Summary
    The paper considers the eigenvalue problem -Δu-αu+λg(x)u=0 withu∈H1(RN),u≠0 where ∞, λ ∈ and  g(x)≡0 on Ω¯,   g(x) ∈ (0,1] onRN \ Ω¯  and lim|x|→+∞g(x)=1 for some bounded open set Ω∈RN. Given α>0, does there exist a value of λ>0 for which the problem has a positive solution? It is shown that this occurs if and only if α lies in a certain interval (Γ,ξ1) and that in this case the value of λ is unique, λ=Λ(α). The properties of the function Λ(α) are also discussed