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On the Principal Eigencurve of the p-Laplacian: Stability Phenomena

Published online by Cambridge University Press:  20 November 2018

Abdelouahed El Khalil ,
Said El Manouni  and
Mohammed Ouanan
Abdelouahed El Khalil
Affiliation:
Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, Montréal, [email protected]
Said El Manouni
Affiliation:
Department of Mathematics, Faculty of Sciences Dhar-Mahraz, P.O. Box 1796 Atlas, Fez 30000, [email protected][email protected]
Mohammed Ouanan
Affiliation:
Department of Mathematics, Faculty of Sciences Dhar-Mahraz, P.O. Box 1796 Atlas, Fez 30000, [email protected][email protected]
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Abstract

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We show that each point of the principal eigencurve of the nonlinear problem

$$-{{\Delta }_{p}}u-\text{ }\lambda m(x){{\left| u \right|}^{p-2}}u=\mu {{\left| u \right|}^{p-2}}u\,\,\text{in}\Omega ,$$

is stable (continuous) with respect to the exponent $p$ varying in $\left( 1,\infty \right)$; we also prove some convergence results of the principal eigenfunctions corresponding.

Keywords

35P3035P6035J70p-Laplacian with indefinite weightprincipal eigencurveprincipal eigenvalueprincipal eigenfunctionstability
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 3 , 01 September 2006 , pp. 358 - 370
Copyright
Copyright © Canadian Mathematical Society 2006

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