Existence and multiplicity results for homoclinic orbits of Hamiltonian systems

Electronic Journal of Differential Equations

Volumn 1997, Issue , 1997, Pages 1-19

  Chen, Chao Nien ^a   Tzeng, Shyuh Yaur ^a  

^a NATIONAL CHANGHUA UNIVERSITY OF EDUCATION   (Taiwan)

Author keywords

Calculus of variations; Hamiltonian system; Homoclinic

Indexed keywords

EID: 0007083424     PISSN: 10726691     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. A. Ambrosetti and P.H. Rabinowitz, Dual Variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 394-381.
2. C.-N. Chen, Some existence and bifurcation results for solutions of non-linear Sturm-Liouville eigenvalue problems, Math. Z. 208 (1991), 177-192.
3. V. Coti Zelati, I. Ekeland and E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann. 288 (1990), 133-160.
4. P. Caldiroli and P. Montecchiari, Homoclinic orbits for second order Hamiltonian systems with potential changing sign. Comm. on Appl. Nonlinear Anal. 1 (1994), 97-129.
5. V. Coti Zelati and P.H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J.A.M.S. 4 (1991), 693-727.
6. V. Coti Zelati and P.H. Rabinowitz, Multibump periodic solutions of a family of Hamiltonian systems, Topological Methods in Nonlinear Analysis 4 (1995), 31-57.
7. W.-Y. Ding and W.-M. Ni, On the existence of a positive entire solution of a semilinear elliptic equation, Arch. Rat. Mech. Anal. 91 (1986),283-308.
8. F. Giannoni and P. H. Rabinowitz, On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systems, Nonlinear Differential Equations and Applications 1 (1994), 1-46.
9. P. Montecchiari, Multiplicity of homoclinic solutions for a class of asymptotically periodic second order Hamiltonian systems, Rend. Mat. Acc. Lincei s.9, 4 (1994), 265-271.
10. J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Appl. Math. Sc. 74, Springer, 1989.
11. P. L. Lions, The concentration-compactness principle in the calculus of variations, Rev. Mat. Iberoam. 1 (1985), 145-201.
12. P.H. Rabinowitz and K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z. 206 (1991), 473-479.
13. P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh, 114A (1990), 33-38.
14. P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, C. B. M. S. Regional Conf. Series in Math., No. 65, Amer. Math. Soc., 1986.
15. P.H. Rabinowitz, Homoclinic and heteroclinic orbits for a class of Hamiltonian systems, Calc. Var. 1 (1993), 1-36.
16. P.H. Rabinowitz, Multibump solutions of differential equations: An overview, Chinese Journal of Mathematics 24 (1996), 1-36.
17. E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z. 209 (1992), 27-42.
18. G. Spradlin, Multibump solutions to a Hamiltonian systems with an almost periodic term, Part I: Finding a saddle point, preprint.
19. K. Strobel, Multibump solutions for a class of periodic Hamiltonian systems, University of Wisconsin, Thesis, 1994.