Infinitely many homoclinic orbits of a Hamiltonian system with symmetry

Nonlinear Analysis, Theory, Methods and Applications

Volumn 38, Issue 3, 1999, Pages 391-415

  Ding, Yanheng ^a   Girardi, Mario ^b  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b ROMA TRE UNIVERSITY   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; MATRIX ALGEBRA; SET THEORY; THEOREM PROVING;

HAMILTONIAN SYSTEMS (HS); HOMOCLINIC ORBITS;

COMPUTATIONAL GEOMETRY;

EID: 0033212485     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00204-1     Document Type: Article

References (20)

1. A. Ambrosetti, V. Coti-Zelati, Multiplicité des orbites homoclines pour des systèmes conservatifs, C. R. Acad. Sci. Paris 314 (1992) 601-604.
2. W.A. Coppel, Dichotomies in Stability Theory, Lecture Notes in Maths, vol. 629, Springer, Berlin, 1978.
3. V. Coti-Zelati, I. Ekeland, E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann. 228 (1990) 133-160.
4. V. Coti-Zelati, P.H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc. 4 (1991) 693-727.
5. Y.H. Ding, Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems, Nonlinear Anal. TMA 25 (1995) 1095-1113.
6. Y.H. Ding, M. Girardi, Periodic and homoclinic solutions to a class of Hamiltonian systems with the potentials changing sign, Dynamic Systems Appl. 2 (1993) 131-145.
7. Y.H. Ding, S.J. Li, Homoclinic orbits for first order Hamiltonian systems, J. Math. Anal. Appl. 189 (1995) 585-601.
8. Y.H. Ding, M. Willem, Homoclinic orbits of a Hamiltonian system, ZAMP, to appear.
9. H. Hofer, K. Wysocki, First-order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems, Math. Ann. 228 (1990) 483-503.
10. T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
11. W. Kryszewski, A. Szulkin, Generalized linking theorem with an application to semilinear Schrödinger equation, Preprint.
12. P.L. Lions, The concentration-compactness principle in the calculus of variations, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 1 (1984) 109-145 and 223-283.
13. W. Omana, M. Willem, Homoclinic orbits for a class of Hamiltonian systems, Differential Integral Equations 5 (1992) 1115-1120.
14. P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh 114 (1990) 33-38.
15. P.H. Rabinowitz, K. Tànaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z. 206 (1991) 473-499.
16. N. Rouche, J. Mawhin, Équations Différentielles Ordinaires, Masson et Cie, 1973.
17. E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z. 209 (1992) 27-42.
18. K. Tanaka, Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits, J. Differential Equations 94 (1991) 315-339.
19. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
20. M. Willem, Minimax Theorems, Birkhäuser, Basel, 1996.