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On the non-existence of homoclinic orbits
for a class of infinite dimensional
Hamiltonian systems


Authors: Ph. Clément and R. C. A. M. van der Vorst
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
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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 Poho\v{z}aev type identity.


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Additional 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

DOI: https://doi.org/10.1090/S0002-9939-97-03696-4
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
Article copyright: © Copyright 1997 American Mathematical Society