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A minimax theorem in the presence of unbounded Palais-Smale sequences

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Abstract

In a reflexive Banach space we consider a family of functionals that may admit unbounded Palais-Smale sequences. Under some structural conditions we provide a suitable Deformation Lemma that is obtained by modifying the classical pseudo-gradient flow. This leads to a variant of the minimax principle in the Lusternik-Schnirelman Theory.

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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, 50931, Köln, Germany

    Jiří Horák

  2. Mathematics Department, The City University of New York, CSI Staten Island, NY, 10314, USA

    Marcello Lucia

Authors
  1. Jiří Horák
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  2. Marcello Lucia
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Correspondence to Jiří Horák.

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Horák, J., Lucia, M. A minimax theorem in the presence of unbounded Palais-Smale sequences. Isr. J. Math. 172, 125–143 (2009). https://doi.org/10.1007/s11856-009-0067-0

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  • DOI: https://doi.org/10.1007/s11856-009-0067-0

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