Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems

Journal of Mathematical Analysis and Applications

Volumn 328, Issue 1, 2007, Pages 380-389

  Jiang, Qin ^a   Tang, Chun Lei ^a  

^a SOUTHWEST UNIVERSITY   (China)

Author keywords

Condition (C); Hamiltonian systems; Periodic solution; Saddle Point Theorem; Subharmonic solutions; Subquadratic

Indexed keywords

EID: 33845885151     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.05.064     Document Type: Article

References (19)

1. Avila A.I., and Felmer P.L. Periodic and subharmonic solutions for a class of second-order Hamiltonian systems. Dynam. Systems Appl. 3 4 (1994) 519-536
2. Cerami G. An existence criterion for the critical points on unbounded manifolds. Istit. Lombardo Accad. Sci. Lett. Rend. A 112 2 (1978) 332-336 (in Italian)
3. Clarke F.H., and Ekeland I. Nonlinear oscillations and boundary value problems for Hamiltonian systems. Arch. Ration. Mech. Anal. 78 4 (1982) 315-333
4. Costa D.G., and Magalhaes C.A. Variational elliptic problems which are nonquadratic at infinity. Nonlinear Anal. 23 11 (1994) 1401-1412
5. El Amrouss A.R., and Moussaoui M. Minimax principles for critical-point theory in applications to quasilinear boundary-value problems. Electron. J. Differential Equations 2000 18 (2000) 1-9
6. Felmer P.L., and de B. e. Silva E.A. Subharmonics near an equilibrium for some second-order Hamiltonian systems. Proc. Roy. Soc. Edinburgh Sect. A 123 5 (1993) 819-834
7. Fonda A., and Lazer A.C. Subharmonic solutions of conservative systems with nonconvex potentials. Proc. Amer. Math. Soc. 115 1 (1992) 183-190
8. Fonda A., Ramos M., and Willem M. Subharmonic solutions for second-order differential equations. Topol. Methods Nonlinear Anal. 1 1 (1993) 49-66
9. Hirano N. Subharmonic solutions for second-order differential systems. J. Math. Anal. Appl. 196 1 (1995) 266-281
10. Hirano N., and Wang Z.-Q. Subharmonic solutions for second-order Hamiltonian systems. Discrete Contin. Dyn. Syst. 4 3 (1998) 467-474
11. Jiang M.-Y. Subharmonic solutions of second-order subquadratic Hamiltonian systems with potential changing sign. J. Math. Anal. Appl. 244 2 (2000) 291-303
12. Long Y.M. Nonlinear oscillations for classical Hamiltonian systems with bi-even subquadratic potentials. Nonlinear Anal. 24 12 (1995) 1665-1671
13. Mawhin J., and Willem M. Critical Point Theory and Hamiltonian Systems. Appl. Math. Sci. vol. 74 (1989), Springer-Verlag, New York
14. Rabinowitz P.H. On subharmonic solutions of Hamiltonian systems. Comm. Pure Appl. Math. 33 5 (1980) 609-633
15. Tang C.-L., and Wu X.-P. Subharmonic solutions for nonautonomous sublinear second-order Hamiltonian systems. J. Math. Anal. Appl. 304 1 (2005) 383-393
16. Tang C.-L., and Wu X.-P. Periodic solutions for a class of nonautonomous subquadratic second-order Hamiltonian systems. J. Math. Anal. Appl. 275 2 (2002) 870-882
17. Tang C.-L., and Wu X.-P. Notes on periodic solutions of subquadratic second-order systems. J. Math. Anal. Appl. 285 1 (2003) 8-16
18. Wang Q., Wang Z.-Q., and Shi J.-Y. Subharmonic oscillations with prescribed minimal period for a class of Hamiltonian systems. Nonlinear Anal. 28 7 (1997) 1273-1282
19. Willem M. Subharmonic oscillations of convex Hamiltonian systems. Nonlinear Anal. 9 11 (1985) 1303-1311