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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the non-existence of homoclinic orbits for a class of infinite dimensional Hamiltonian systems
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by Ph. Clément and R. C. A. M. van der Vorst
Proc. Amer. Math. Soc. 125 (1997), 1167-1176
DOI: https://doi.org/10.1090/S0002-9939-97-03696-4

Abstract:

We prove that for a class of infinite dimensional Hamiltonian systems certain homoclinic connections to the origin cease to exist when the non-linearities have ‘super-critical’ growth. The proof is based on a variational principle and a Pohožaev type identity.
References
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Bibliographic Information
  • Ph. Clément
  • Affiliation: Delft University of Technology, Faculty of Technical Mathematics and Informatics, Delft, The Netherlands
  • R. C. A. M. van der Vorst
  • Affiliation: Center for Dynamical Systems, Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia 30332-0190
  • Received by editor(s): October 25, 1995
  • Additional Notes: This work was supported by the Netherlands Organization for Scientific Research, NWO and EC-HCM project Reaction–Diffusion Equations ERBCHRXCT930409.
  • Communicated by: Hal L. Smith
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 1167-1176
  • MSC (1991): Primary 35J50, 35J55, 46E35
  • DOI: https://doi.org/10.1090/S0002-9939-97-03696-4
  • MathSciNet review: 1363415