Generalized eigenvalue problem for totally discontinuous operators

Jean-Michel Rakotoson

doi:10.3934/dcds.2010.28.343

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2010, Volume 28, Issue 1: 343-373. Doi: 10.3934/dcds.2010.28.343

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Generalized eigenvalue problem for totally discontinuous operators

Jean-Michel Rakotoson^1,

1.
UMR 6086 CNRS. Laboratoire de Mathématiques - Université de Poitiers - SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, BP30179 - 86962 Futuroscope Chasseneuil Cedex

Received: August 31, 2009

Revised: October 31, 2009

Published: February 2010

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Abstract

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

-div→_p(δφ _i(x,δu/δx_i))=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.

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Mathematics Subject Classification: Primary: 35P30, 47J10, 35R70; Secondary: 46N10, N9N99, 46B50.

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