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September/October 2009 Maximum and antimaximum principles: beyond the first eigenvalue
J. Fleckinger, J.-P. Gossez, F. de Thélin
Differential Integral Equations 22(9/10): 815-828 (September/October 2009).

Abstract

We consider the Dirichlet problem (*)$ -\bigtriangleup u=\mu u+f$ in $\Omega,u=0$ on $\partial\Omega$. Let $\widehat{\lambda}$ be an eigenvalue, with $\widehat{\varphi}$ an associated eigenfunction. Under suitable assumptions on $f$ and on the nodal domains of $\widehat{\varphi}$, we show that, if $\mu$ is sufficiently close to $\widehat{\lambda}$, then the solution $u$ of (*) has the same number of nodal domains as $\widehat{\varphi}$, and moreover the nodal domains of $u$ appear as small deformations of those of $\widehat{\varphi}$.

Citation

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J. Fleckinger. J.-P. Gossez. F. de Thélin. "Maximum and antimaximum principles: beyond the first eigenvalue." Differential Integral Equations 22 (9/10) 815 - 828, September/October 2009.

Information

Published: September/October 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35128
MathSciNet: MR2553057

Subjects:
Primary: 35J25
Secondary: 35B50, 35P05

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 9/10 • September/October 2009
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