Remarks on a polyharmonic eigenvalue problem

Patrizia Pucci; Vicenţiu Rădulescu

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

Patrizia Pucci ¹ ; Vicenţiu Rădulescu ^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, Volume 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 :

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

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     author = {Patrizia Pucci and Vicen\c{t}iu R\u{a}dulescu},
     title = {Remarks on a polyharmonic eigenvalue problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {161--164},
     publisher = {Elsevier},
     volume = {348},
     number = {3-4},
     year = {2010},
     doi = {10.1016/j.crma.2010.01.013},
     language = {en},
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%A Vicenţiu Rădulescu
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Patrizia Pucci; Vicenţiu Rădulescu. Remarks on a polyharmonic eigenvalue problem. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 161-164. doi : 10.1016/j.crma.2010.01.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.01.013/

Bibliographie
Cité par

[1] F. Gazzola; H.-C. Grunau 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] P. Pucci; J. Serrin 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] M. Struwe 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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