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Limit Cases of the Palais-Smale Condition

  • Michael Struwe
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge book series (MATHE3, volume 34)

Abstract

Condition (P.-S.) may seem rather restrictive. Actually, as Hildebrandt [4; p. 324] records, for quite a while many mathematicians felt convinced that inspite of its success in dealing with one-dimensional variational problems like geodesics (see Birkhoff’s Theorem I.4.4, for example, or Palais’ [3] work on closed geodesics), the Palais-Smale condition could never play a role in the solution of “interesting” variational problems in higher dimensions.

Keywords

Riemannian Surface Dirichlet Problem Nontrivial Solution Limit Case Homotopy Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Michael Struwe
    • 1
  1. 1.Mathematik, ETH-ZentrumETH ZürichZürichSwitzerland

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