Limit Cases of the Palais-Smale Condition

Michael Struwe
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Michael Struwe: Mathematik, ETH Zürich, ETH-Zentrum

Chapter Chapter III in Variational Methods, 1990, pp 154-210 from Springer

Abstract: Abstract Condition (P.-S.) may seem rather restrictive. Actually, as Hildebrandt [4; p. 324] records, for quite a while many mathematicians felt convinced that in-spite 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 (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-3-662-02624-3_3

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