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On the spectrum of a nonlinear planar problem

Gladiali, Francesca Maria and Grossi, Massimo (2009) On the spectrum of a nonlinear planar problem. Annales de l'Institut Henri Poincaré. (C) Analyse non linéaire, Vol. 26 (1), p. 191-222. ISSN 0294-1449. Article.

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DOI: 10.1016/j.anihpc.2007.10.004


We consider the eigenvalue problem

υ = λμeυ ---in Ω,
||υ|| = 1------------------------------------(0.1)
υ = 0 ------------on ∂Ω,

where Ω is a bounded smooth domain of R2, λ>0 is a real parameter and is a solution of

uλ = λe-----in Ω,
= 0-----------on ∂Ω

such that λ∫Ω e →8π as λ→0. In this paper we study the asymptotic behavior of the eigenvalues μ of (0.1) as λ→0. Moreover some explicit estimates for the four first eigenvalues and eigenfunctions are given.
Other related results as the Morse index of the solution will be proved.

Item Type:Article
ID Code:1527
Uncontrolled Keywords:Eigenvalues, eigenfuntions, Morse index
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Divisions:001 Università di Sassari > 03 Istituti > Matematica e fisica
Publisher:Elsevier Masson
Additional Information:Supported by M.I.U.R., project “Variational methods and nonlinear differential equations”.
Deposited On:18 Aug 2009 10:05

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