NDLI: Interacting near-solutions of a hamiltonian system

Content Provider	Springer Nature Link
Author	Spradlin, Gregory S.
Copyright Year	2004
Abstract	A Hamiltonian system with a superquadratic potential is examined. The system is asymptotic to an autonomous system. The difference between the Hamiltonian system and the “problem at infinity,” the autonomous system, may be large, but decays exponientially. The existence of a nontrivial solution homoclinic to zero is proven. Many results of this type rely on a monotonicity condition on the nonlinearity, not assumed here, which makes the problem resemble in some sense the special case of homogeneous (power) nonlinearity. The proof employs variational, minimax arguments. In some similar results requiring the monotonicity condition, solutions inhabit a manifold homeomorphic to the unit sphere in a the appropriate Hilbert space of functions. An important part of the proof here is the construction of a similar set, using only the mountain-pass geometry of the energy functional. Another important element is the interaction between functions resembling widely separated solutions of the autonomous problem.
Starting Page	447
Ending Page	464
Page Count	18
File Format	PDF
ISSN	09442669
Journal	Calculus of Variations and Partial Differential Equations
Volume Number	22
Issue Number	4
e-ISSN	14320835
Language	English
Publisher	Springer-Verlag
Publisher Date	2004-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Analysis Systems Theory, Control Calculus of Variations and Optimal Control Optimization Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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