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On a nonlinear eigenvalue problem in OrliczSobolev spaces

Published online by Cambridge University Press:  12 July 2007

J.-P. Gossez  and
R. Mansevich
J.-P. Gossez
Affiliation:
Dpartement de Mathmatiques, Universit Libre de Bruxelles, CP 214, 1050 Bruxelles, Belgium ([email protected])
R. Mansevich
Affiliation:
Centro de Modelamiento Matemtico and Departamento de Ingeniea Matemtica, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile ([email protected])
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Abstract

We consider the eigenvalue problem in an arbitrary OrliczSobolev space. We show that the existence of an eigenvalue can be derived from a generalized version of Lagrange multiplier rule. Our approach also applies to more general problems. We emphasize that no 2 condition is imposed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 4 , August 2002 , pp. 891 - 909
Copyright
Copyright © Royal Society of Edinburgh 2002

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