Scattered homoclinics to a class of time-recurrent Hamiltonian systems

Gregory S. Spradlin

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 3, page 528-537
  • ISSN: 1292-8119

Abstract

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A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.

How to cite

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Spradlin, Gregory S.. "Scattered homoclinics to a class of time-recurrent Hamiltonian systems." ESAIM: Control, Optimisation and Calculus of Variations 13.3 (2007): 528-537. <http://eudml.org/doc/249983>.

@article{Spradlin2007,
abstract = { A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line. },
author = {Spradlin, Gregory S.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Mountain pass theorem; Palais-Smale sequences; almost periodic; Hamiltonian system; mountain pass theorem; almost periodicity; Hamiltonian system},
language = {eng},
month = {6},
number = {3},
pages = {528-537},
publisher = {EDP Sciences},
title = {Scattered homoclinics to a class of time-recurrent Hamiltonian systems},
url = {http://eudml.org/doc/249983},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Spradlin, Gregory S.
TI - Scattered homoclinics to a class of time-recurrent Hamiltonian systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/6//
PB - EDP Sciences
VL - 13
IS - 3
SP - 528
EP - 537
AB - A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.
LA - eng
KW - Mountain pass theorem; Palais-Smale sequences; almost periodic; Hamiltonian system; mountain pass theorem; almost periodicity; Hamiltonian system
UR - http://eudml.org/doc/249983
ER -

References

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  1. V. Coti Zelati and P. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. J. Amer. Math. Soc.4 (1991) 693–627.  
  2. P. Montecchiari, M. Nolasco and S. Terracini, Multiplicity of homoclinics for a class of time recurrent second order Hamiltonian systems. Calc. Var.5 (1997) 523–555.  
  3. P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, C. B. M. S. Regional Conf. Series in Math.65. Amer. Math. Soc., Providence (1986).  
  4. G. Spradlin, Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity. Electronic J. Diff. Equ.2004 (2004) 1–13.  
  5. E. Serra, M. Tarallo and S. Terracini, On the existence of homoclinic solutions to almost periodic second order systems. Ann. l'Instit. Henri Poincaré13 (1996) 783–812.  

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