Scattered homoclinics to a class of time-recurrent hamiltonian systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 528-537.

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.

DOI : 10.1051/cocv:2007023
Classification : 34C37, 47J30
Mots-clés : mountain pass theorem, Palais-Smale sequences, almost periodic, hamiltonian system 
@article{COCV_2007__13_3_528_0,
     author = {Spradlin, Gregory S.},
     title = {Scattered homoclinics to a class of time-recurrent hamiltonian systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {528--537},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {3},
     year = {2007},
     doi = {10.1051/cocv:2007023},
     mrnumber = {2329174},
     zbl = {1124.37037},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2007023/}
}
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
PY  - 2007
SP  - 528
EP  - 537
VL  - 13
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2007023/
DO  - 10.1051/cocv:2007023
LA  - en
ID  - COCV_2007__13_3_528_0
ER  - 
%0 Journal Article
%A Spradlin, Gregory S.
%T Scattered homoclinics to a class of time-recurrent hamiltonian systems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2007
%P 528-537
%V 13
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv:2007023/
%R 10.1051/cocv:2007023
%G en
%F COCV_2007__13_3_528_0
Spradlin, Gregory S. Scattered homoclinics to a class of time-recurrent hamiltonian systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 528-537. doi : 10.1051/cocv:2007023. http://www.numdam.org/articles/10.1051/cocv:2007023/

[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. | Zbl

[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. | Zbl

[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). | MR | Zbl

[4] G. Spradlin, Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity. Electronic J. Diff. Equ. 2004 (2004) 1-13. | Zbl

[5] E. Serra, M. Tarallo and S. Terracini, On the existence of homoclinic solutions to almost periodic second order systems. Ann. l'Instit. Henri Poincaré 13 (1996) 783-812. | Numdam | Zbl

Cité par Sources :