Non linear eigenvalue problems

Didier Robert (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Didier Robert. Non linear eigenvalue problems. 2004. ⟨hal-00003472⟩