# Scattered homoclinics to a class of time-recurrent Hamiltonian systems

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

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

## Access Full Article

top## Abstract

top## How to cite

topSpradlin, 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

top- V. Coti Zelati and P. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. J. Amer. Math. Soc.4 (1991) 693–627. Zbl0744.34045
- 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. Zbl0886.58014
- 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). Zbl0609.58002
- G. Spradlin, Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity. Electronic J. Diff. Equ.2004 (2004) 1–13. Zbl1065.34039
- 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. Zbl0873.58032

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.