Homoclinic orbits in a first order superquadratic hamiltonian system: Convergence of subharmonic orbits
TLDR
In this article, the existence of homoclinic orbits for a first order Hamiltonian system z = JH z (t, z) is studied and a nontrivial solution z∞(t) and subharmonic solutions (zT(t))TϵN (i.e., 2πT-periodic solutions) of (HS) such that ZT → Z∞ (t) in Cloc1(R, R 2N) as T → ∞.About:
This article is published in Journal of Differential Equations.The article was published on 1991-12-01 and is currently open access. It has received 94 citations till now. The article focuses on the topics: Homoclinic orbit & Hamiltonian system.read more
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Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials
TL;DR: In this article, the first author was supported by Ministero P. I. gruppo 40% "Calcolo delle variazioni" and the second author's research was sponsored in part by the U.S. Army Research Office under contract #DAAL03-87-K-0043, the National Science Foundation under Grant #MCS-8110556 and the Office of Naval Research under grant #N00014-88-KO134.
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Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems
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Stationary states of the nonlinear Dirac equation: a variational approach
Maria J. Esteban,Eric Séré +1 more
TL;DR: In this article, the existence of stationary solutions of nonlinear Dirac equations is proved by using a general variational technique, which enables us to consider nonlinearities which are not necessarily compatible with symmetry reductions.
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Homoclinic Orbits for Asymptotically Linear Hamiltonian Systems
Andrzej Szulkin,Wenming Zou +1 more
TL;DR: In this paper, the existence of homoclinic orbits for first order time-dependent Hamiltonian systems was studied, where H(z, t) depends periodically on t and Hz(z, t) is asymptotically linear in z as |z|→∞.
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Looking for the Bernoulli shift
TL;DR: In this article, a result on the topological entropy of a large class of Hamiltonian systems was proved by constructing "multibump" homoclinic solutions to the problem.
References
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Book
Minimax methods in critical point theory with applications to differential equations
TL;DR: The mountain pass theorem and its application in Hamiltonian systems can be found in this paper, where the saddle point theorem is extended to the case of symmetric functionals with symmetries and index theorems.
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Homoclinic orbits for a class of Hamiltonian systems
TL;DR: In this paper, the second order Hamiltonian system (HS) has a homoclinic orbit q emanating from 0, where q ∊ ℝn and V ∊ C1 (ℝ ×ℽn ℽ) is T periodic in t. The orbit q is obtained as the limit as k → ∞ of 2kT periodic solutions (i.e. subharmonics) qk of (HS).
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A variational approach to homoclinic orbits in Hamiltonian systems
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Some results on connecting orbits for a class of Hamiltonian systems.
TL;DR: In this article, the existence of connecting orbits for a certain Hamiltonian system as well as its time dependent analogue is established for the autonomous case, where the main assumption is that V has a global maximum, e.g. at X = O and we find a various kinds of orbits terminating at O.