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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Basis properties of eigenfunctions of the $ p$-Laplacian


Authors: Paul Binding, Lyonell Boulton, Jan Cepicka, Pavel Drábek and Petr Girg
Journal: Proc. Amer. Math. Soc. 134 (2006), 3487-3494
MSC (2000): Primary 34L30; Secondary 34L10, 42A65
Published electronically: June 27, 2006
MathSciNet review: 2240660
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Abstract | References | Similar Articles | Additional Information

Abstract: For $ p\geqslant \frac{12}{11}$, the eigenfunctions of the non-linear eigenvalue problem for the $ p$-Laplacian on the interval $ (0,1)$ are shown to form a Riesz basis of $ L_2(0,1)$ and a Schauder basis of $ L_q(0,1)$ whenever $ 1<q<\infty$.


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Additional Information

Paul Binding
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4

Lyonell Boulton
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4

Jan Cepicka
Affiliation: Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

Pavel Drábek
Affiliation: Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

Petr Girg
Affiliation: Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08001-4
PII: S 0002-9939(06)08001-4
Keywords: $p$-Laplacian eigenvalues, eigenfunction completeness.
Received by editor(s): May 5, 2004
Received by editor(s) in revised form: October 19, 2004
Published electronically: June 27, 2006
Additional Notes: The research of the first author was supported by I. W. Killam Foundation and NSERC of Canada
The second author was supported by a PIMS Postdoctoral Fellowship at the University of Calgary
The research of the third, fourth, and fifth authors was supported by GAČR, no. 201/03/0671
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2006 American Mathematical Society