Subharmonic solutions of second order subquadratic Hamiltonian systems with potential changing sign

Journal of Mathematical Analysis and Applications

Volumn 244, Issue 2, 2000, Pages 291-303

  Jiang, Mei Yue ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034654696     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6687     Document Type: Article

References (19)

1. Avila A., Felmer P. Periodic and subharmonic solutions for a class of Hamiltonian systems. Dynam. Systems Appl. 3:1994;519-536.
2. Naoum A. K. Ben, Troestler C., Willem M. Existence and multiple results for homogeneous second order differential equations. J. Differential Equations. 112:1994;239-249.
3. Chen G., Long Y. Periodic solutions of superquadratic Hamiltonian systems of second order with mean value zero. Chinese Ann. Math. 19:1998;525-532.
4. Ekeland I. Convexity Methods in Hamiltonian Mechanics. 1990;Springer-Verlag, Berlin/New York.
5. Felmer P. Periodic solutions of "superquadratic" Hamiltonian systems. J. Differential Equations. 102:1993;188-207.
6. Felmer P., Silva E. Subharmonic solutions near an equilibrium for some second order Hamiltonian systems. Proc. Roy. Soc. Edinburgh Sect. A. 123:1993;819-834.
7. Girardi M., Matzeu M. Existence and multiplicity results for periodic solutions of superquadratic Hamiltonian systems where the potential changes sign. Nonlinear Differential Equations Appl. 2:1995;35-61.
8. 2 have different superquadratic growths. Proc. Local and Variational Methods on Hamiltonian Systems. 1995;World Scientific, Singapore. p. 65-76.
9. Jiang M.-Y. Symplectic transformations and periodic solutions of Hamiltonian systems. J. Math. Anal. Appl. 225:1998;133-143.
10. Jiang M.-Y. On a theorem of Mather and Aubry-Mather sets for planar Hamiltonian systems. Sci. China. A 42:1999;1121-1128.
11. Jiang M.-Y., Pei M.-L. Mather sets for superlinear plane Hamiltonian systems. Dynam. Systems Appl. 2:1993;189-200.
12. Lassoued L. Solutions periodique d'un systeme differentiel nonlineaire du second ordre avec chagement de signe. Ann. Mat. Pura Appl. 156:1990;76-111.
13. Lassoued L. Periodic solutions of a second order superquadratic system with change of sign of the potential. J. Differential Equations. 93:1991;1-18.
14. Liu B. The stability of the equilibrium of a conservative system. J. Math. Anal. Appl. 202:1996;133-149.
15. Mather J. N. Action Minimizing Orbits in Hamiltonian Systems. Lecture Notes in Mathematics. 1589:1991;Springer-Verlag, Berlin.
16. Pei M. L. Mather sets for superlinear Duffing equation. Sci. China A. 36:1993;524-537.
17. Pei M. L. Mather sets for finite twist maps of a cylinder and semilinear Duffing equation. J. Differential Equations. 113:1994;106-127.
18. Rabinowitz P. H. Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS, Regional Conf. Ser. in Math. 65:1986;Amer. Math. Soc. Providence.
19. Silva E. Subharmonic solutions for subquadratic Hamiltonian systems. J. Differential Equations. 115:1995;120-145.