On the Existence of Positive Eigenvalues for Linear and Nonlinear Equations with Indefinite Weight |
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| Authors: | N Bel Haj Rhouma M Mosbah |
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| Institution: | 1. Institut Préparatoire aux Etudes d'Ingénieurs de Tunis , Tunis, Tunisia;2. Faculté des Sciences de Bizerte , Bizerte, Tunisia |
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| Abstract: | We prove the existence of positive eigenvalues for two types of equations having an indefinite weight. We consider the linear case, and we show the existence of a positive principal eigenvalue corresponding to a positive eigenfunction. For the nonlinear case, we show that the set of positive eigenvalues is an unbounded interval, and that the corresponding eigenfunctions are positive. |
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| Keywords: | Indefinite Weight Kato-class Superharmonic Function Principal Eigenvalue Eigenfunction |
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