manuscripta mathematica

, Volume 19, Issue 2, pp 105–132 | Cite as

Über das Verzweigungsverhalten eines nichtlinearen Eigenwertproblems in der Nähe eines unendlich vielfachen Eigenwertes der Linearisierung

  • Hans -Peter Heinz
Article
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Abstract

We consider a nonlinear operator G=A+R in Hilbert space, where A is linear, bounded and self-adjoint, and R is completely continous with ∥R(x)∥=0(∥x∥) for x→0. We establish various conditions under which an eigenvalue λ0 of A ofinfinite multiplicity is a bifurcation point of the nonlinear eigenvalue problem G(x)=λ x. To this end, we first prove the existence of a certain type of approximation procedure the construction of bifurcation solutions in the case of infinite multiplicity. The existence theorems for the problem G(x)=λ x are then obtained by applying this procedure to various situations.

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Hans -Peter Heinz
    • 1
  1. 1.Fachbereich Mathematik65 Mainz

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