Sturm theorems for degenerate elliptic equations

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 29 Mar 2001 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 129, pages 3,031-3,035 (issn: 0002-9939, eissn: 1088-6826,

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Authors: Allegretto, Walter;

doi: 10.1090/s0002-9939-01-05979-2

Sturm theorems for degenerate elliptic equations

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Abstract

A kind of the Picone identity for a class of degenerate \(p\)-Laplacians are shown. As a consequence, a Sturm comparison theorem about the change sign of generalized solutions is proved. It is the answer to the open question mentioned in \textit{D. R. Dunninger} [Boll. Unione Mat. Ital., VII. Ser., A 9, No. 1, 117-121 (1995; Zbl 0834.35011)]. The paper represents an extension of some related author's works about the Picone identity and its applications to elliptic equations. See for instance: \textit{W. Allegretto} [Ann. Scuola norm. sup. Pisa, Sci. Fis. Mat., III. Ser. 25, 41-46 (1971; Zbl 0225.35013)], \textit{W. Allegretto} and \textit{Y. X. Huang} [Nonlinear Anal., Theory Methods Appl. 32, No. 7, 819-830 (1998; Zbl 0930.35053)].

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University of Alberta
Canada

Keywords

generalized solutions, Sturm theorems, 834, Picone's identity, Generalized solutions to partial differential equations, 225, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, 930, \(p\)-Laplacian

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