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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Ph. Clément; R. C. A. M. van der Vorst
Journal: Proc. Amer. Math. Soc. 125 (1997), 1167-1176.
MSC (1991): Primary 35J50, 35J55, 46E35
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: 10.1090/S0002-9939-97-03696-4
PII: S 0002-9939(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
Copyright of article: Copyright 1997, American Mathematical Society

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