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)


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.


Riemannian Surface Dirichlet Problem Nontrivial Solution Limit Case Homotopy Class 
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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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