Sturm theorems for degenerate elliptic equations (Q2723502)
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scientific article; zbMATH DE number 1614772
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sturm theorems for degenerate elliptic equations |
scientific article; zbMATH DE number 1614772 |
Statements
Sturm theorems for degenerate elliptic equations (English)
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5 July 2001
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Picone's identity
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\(p\)-Laplacian
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generalized solutions
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Sturm theorems
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834
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225
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930
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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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