Remarks on a polyharmonic eigenvalue problem

Pucci, Patrizia; Rădulescu, Vicenţiu

doi:10.1016/j.crma.2010.01.013

Partial Differential Equations

Remarks on a polyharmonic eigenvalue problem
[Remarques sur un problème poly-harmonique de valeurs propres]

Présenté par : Philippe G. Ciarlet

Pucci, Patrizia ¹ ; Rădulescu, Vicenţiu ^2,³

¹ Università degli Studi di Perugia, Dipartimento di Matematica e Informatica, Via Vanvitelli 1, 06123 Perugia, Italy
² Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 014700 Bucharest, Romania
³ Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585 Craiova, Romania

Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 161-164.

Résumé
Abstract

On considère un problème non linéaire de valeurs propres associé à l'opérateur poly-harmonique sur une boule dans $R^{n}$ . Dans cette Note on montre l'existence d'un spectre continu de valeurs propres tel que la valeur propre principale est isolée.

This Note deals with a nonlinear eigenvalue problem involving the polyharmonic operator on a ball in $R^{n}$ . The main result of this Note establishes the existence of a continuous spectrum of eigenvalues such that the least eigenvalue is isolated.

Reçu le : 2009-12-10
Accepté le : 2009-12-30
Publié le : 2010-02-01

DOI : 10.1016/j.crma.2010.01.013

Affiliations des auteurs :

Pucci, Patrizia ¹ ; Rădulescu, Vicenţiu ^{2, 3}

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     title = {Remarks on a polyharmonic eigenvalue problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {161--164},
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Pucci, Patrizia; Rădulescu, Vicenţiu. Remarks on a polyharmonic eigenvalue problem. Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 161-164. doi : 10.1016/j.crma.2010.01.013. http://www.numdam.org/articles/10.1016/j.crma.2010.01.013/

Bibliographie
Cité par

[1] Gazzola, F.; Grunau, H.-C. Critical dimensions and higher order Sobolev inequalities with remainder terms, NoDEA Nonlinear Differential Equations Appl., Volume 8 (2001), pp. 35-44

[2] M. Mihăilescu, V. Rădulescu, Sublinear eigenvalue problems associated to the Laplace operator revisited, Israel J. Math., in press

[3] Pucci, P.; Serrin, J. Remarks on the first eigenspace for polyharmonic operators, Atti Sem. Mat. Fis. Univ. Modena (Proc. 1986–1987 Focused Research Program on Spectral Theory and Boundary Value Problems), Volume 36 (1988), pp. 107-117 (and, vol. 3, 1989, pp. 135-145 Report ANL-87-26)

[4] Struwe, M. Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin, 2008

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