Non linear eigenvalue problems

In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non trivial eigenstates for models coming from analytic theory of s...

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Bibliographic Details
Main Author Robert, Didier
Format Journal Article
LanguageEnglish
Published 06.12.2004
Subjects
Mathematics - Analysis of PDEs
Mathematics - Mathematical Physics
Physics - Mathematical Physics
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Summary:In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non trivial eigenstates for models coming from analytic theory of smoothness for P.D.E. We shall review some old results and present recent improvements on this subject.
DOI:10.48550/arxiv.math-ph/0412015