Ljusternik-Schnirelman Theory and the Existence of Several Eigenvectors

  • Eberhard Zeidler

Abstract

In Chapter 43 we proved the existence of an eigenvector. Now we concern ourselves with the eigenvalue problem
(1)
and we will prove the existence of several eigenvectors for (1) within the generalized context of the Courant maximum-minimum principle. In this connection, in an essential way, we use the fact that A and B are odd potential operators, i.e., A = F′, B = G′, and A(− μ) = − A(μ), B(−μ) = − B(μ) for all μX. We have already explained the basic idea of the Ljusternik-Schnirelman theory in Section 37.26, and we recommend that the reader first study Section 37.26 again.

Keywords

Manifold Assure Hull 

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References to the Literature

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Application to the existence of geodesies

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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Eberhard Zeidler
    • 1
  1. 1.Sektion MathematikLeipzigGerman Democratic Republic

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