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    Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation
March  2010, 28(1): 343-373. doi: 10.3934/dcds.2010.28.343

Generalized eigenvalue problem for totally discontinuous operators

1. 

UMR 6086 CNRS. Laboratoire de Mathématiques - Université de Poitiers - SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, BP30179 - 86962 Futuroscope Chasseneuil Cedex, France

Received  September 2009 Revised  November 2009 Published  April 2010

We introduce the notion of →p -multivoque Leray-Lions operator

-div→p(δφ i(x,δu/δxi))=Au

on a Banach-Sobolev function space V→p and we study the generalized eigenvalue problem Au=λδj(u). Here δφ i (resp. δj) denotes the subdifferential in the sense of convex analysis or more generally in the sense of H. Clarke.

Citation: Jean-Michel Rakotoson. Generalized eigenvalue problem for totally discontinuous operators. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 343-373. doi: 10.3934/dcds.2010.28.343
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