1999 On the closed solution to some nonhomogeneous eigenvalue problems with $p$-Laplacian
Pavel Drábek, Raúl Manásevich
Differential Integral Equations 12(6): 773-788 (1999). DOI: 10.57262/die/1367241475

Abstract

We deal with the Dirichlet, Neumann and periodic eigenvalue problems for the equation $$ \quad(|u'|^{p-2}u')' +\lambda |u|^{q-2}u=0, \text{\quad on~~}(0,T), $$ where $T>0,$ $\lambda>0,$ and $p,q>1.$ For those problems we obtain a complete description of the spectra and a closed form representation of the corresponding eigenfunctions. As an application of our results we present sharp Poincar\'e and Wirtinger inequalities for the imbeddings $W_0^{1,p}(0,T)$ into $L^q(0,T)$ and $W_T^{1,p}(0,T)$ into $L^q(0,T),$ respectively.

Citation

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Pavel Drábek. Raúl Manásevich. "On the closed solution to some nonhomogeneous eigenvalue problems with $p$-Laplacian." Differential Integral Equations 12 (6) 773 - 788, 1999. https://doi.org/10.57262/die/1367241475

Information

Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1015.34071
MathSciNet: MR1728030
Digital Object Identifier: 10.57262/die/1367241475

Subjects:
Primary: 34B15
Secondary: 34C25 , 34L30 , 47J30

Rights: Copyright © 1999 Khayyam Publishing, Inc.

Vol.12 • No. 6 • 1999
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