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Subharmonic solutions for nonautonomous sublinear second order Hamiltonian systems. (English) Zbl 1076.34049
The authors prove the existence of large amplitude subharmonic solutions to some second order systems of differential equations, generalizing some previous work on this subject. The method of proof is variational.

MSC:
34C25Periodic solutions of ODE
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References:
[1] Avila, A. I.; Felmer, P. L.: Periodic and subharmonic solutions for a class of second order Hamiltonian systems. Dynam. systems appl. 3, 519-536 (1994) · Zbl 0815.34025
[2] Cac, N. P.; Lazer, A. C.: On second order, periodic, symmetric, differential systems having subharmonics of all sufficiently large orders. J. differential equations 127, 426-438 (1996) · Zbl 0853.34039
[3] Clarke, F. H.; Ekeland, I.: Nonlinear oscillations and boundary value problems for Hamiltonian systems. Arch. rational mech. Anal. 78, 315-333 (1982) · Zbl 0514.34032
[4] Felmer, P. L.; De B. E. Silva, E. A.: Subharmonics near an equilibrium for some second-order Hamiltonian systems. Proc. roy. Soc. Edinburgh sect. A 123, 819-834 (1993) · Zbl 0802.34043
[5] Fonda, A.; Lazer, A. C.: Subharmonic solutions of conservative systems with nonconvex potentials. Proc. amer. Math. soc. 115, 183-190 (1992) · Zbl 0752.34027
[6] Fonda, A.; Ramos, M.; Willem, M.: Subharmonic solutions for second order differential equations. Topol. methods nonlinear anal. 1, 49-66 (1993) · Zbl 0803.34029
[7] Giannoni, F.: Periodic solutions of dynamical systems by a saddle point theorem of rabinowitz. Nonlinear anal. 13, 707-719 (1989) · Zbl 0729.58044
[8] Hirano, N.: Subharmonic solutions for second order differential systems. J. math. Anal. appl. 196, 266-281 (1995) · Zbl 0847.34047
[9] Hirano, N.; Wang, Z. Q.: Subharmonic solutions for second order Hamiltonian systems. Discrete contin. Dynam. systems 4, 467-474 (1998) · Zbl 0954.34033
[10] Jiang, M. Y.: Subharmonic solutions of second order subquadratic Hamiltonian systems with potential changing sign. J. math. Anal. appl. 244, 291-303 (2000) · Zbl 0982.37064
[11] Mawhin, J.; Willem, M.: Critical point theory and Hamiltonian systems. (1989) · Zbl 0676.58017
[12] Rabinowitz, P. H.: On subharmonic solutions of Hamiltonian systems. Comm. pure appl. Math. 33, 609-633 (1980) · Zbl 0425.34024
[13] Serra, E.; Tarallo, M.; Terracini, S.: Subharmonic solutions to second-order differential equations with periodic nonlinearities. Nonlinear anal. 41, 649-667 (2000) · Zbl 0985.34033
[14] Tang, C. L.: Periodic solutions for nonautonomous second order systems with sublinear nonlinearity. Proc. amer. Math. soc. 126, 3263-3270 (1998) · Zbl 0902.34036
[15] Tang, C. L.; Wu, X. P.: Periodic solutions for second order systems with not uniformly coercive potential. J. math. Anal. appl. 259, 386-397 (2001) · Zbl 0999.34039
[16] Wang, Q.; Wang, Z. Q.; Shi, J. Y.: Subharmonic oscillations with prescribed minimal period for a class of Hamiltonian systems. Nonlinear anal. 28, 1273-1282 (1997) · Zbl 0872.34022
[17] Willem, M.: Periodic oscillations of odd second order Hamiltonian systems. Boll. un. Mat. ital. B (6) 3, 293-304 (1984) · Zbl 0582.58014
[18] Willem, M.: Subharmonic oscillations of convex Hamiltonian systems. Nonlinear anal. 9, 1303-1311 (1985) · Zbl 0579.34030