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• W1964536812 abstract "We investigate the existence, multiplicity and bifurcation of solutions of a model nonlinear degenerate elliptic differential equation: −x2u″=λu+|u|p−1 uin (0, 1);u(0)=u(1)=0. This model is related to a simplified version of the nonlinear Wheeler–DeWitt equation as it appears in quantum cosmological models. We prove the existence of multiple positive solutions. More precisely, we show that there exists an infinite number of connected branches of solutions which bifurcate from the bottom of the essential spectrum of the corresponding linear operator. Nous étudions ici l'existence, multiplicité et propriétés de bifurcation des solutions d'un problème elliptique dégénéré: −x2u″=λu+|u|p−1 uin (0, 1);u(0)=u(1)=0. Ce problème modèle est proche d'une version simplifiée et non-linéaire de l'équation de Wheeler–DeWitt, utilisée dans des modèles de Cosmologie quantique. Nous prouvons l'existence d'une infinité de branches de solutions qui bifurquent à partir de l'infimum du spectre continu de l'opérateur linéaire correspondant." @default.
• W1964536812 created "2016-06-24" @default.
• W1964536812 creator A5012342973 @default.
• W1964536812 creator A5084149439 @default.
• W1964536812 date "1997-02-01" @default.
• W1964536812 modified "2023-10-02" @default.
• W1964536812 title "Existence and Bifurcation of Solutions for an Elliptic Degenerate Problem" @default.
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• W1964536812 doi "https://doi.org/10.1006/jdeq.1996.3165" @default.
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