We consider the eigenvalue problem [GRAPHICS] where Omega is a bounded smooth domain of R(2), lambda > 0 is a real parameter and it is a solution of [GRAPHICS] such that lambda integral Omega EU lambda -> 8 pi as lambda -> 0. In this paper we Study theasymptotic behavior of the eigenvalues mu of(0, 1) as lambda -> 0. Moreover some explicit estimates for the four first eigenvalues and eigenfunctions are given. Other related results as the Morse index of the solution u(lambda) will be proved. (c) 2007 Flsevier Masson SAS. All rights reserved.
On the spectrum of a nonlinear planar problem / Grossi, Massimo; Gladiali, Francesca Maria. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 26:1(2009), pp. 191-222. [10.1016/j.anihpc.2007.10.004]
On the spectrum of a nonlinear planar problem
GROSSI, Massimo;GLADIALI, Francesca Maria
2009
Abstract
We consider the eigenvalue problem [GRAPHICS] where Omega is a bounded smooth domain of R(2), lambda > 0 is a real parameter and it is a solution of [GRAPHICS] such that lambda integral Omega EU lambda -> 8 pi as lambda -> 0. In this paper we Study theasymptotic behavior of the eigenvalues mu of(0, 1) as lambda -> 0. Moreover some explicit estimates for the four first eigenvalues and eigenfunctions are given. Other related results as the Morse index of the solution u(lambda) will be proved. (c) 2007 Flsevier Masson SAS. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
