## Periodic solutions for a class of nonautonomous second order Hamiltonian systems.(English)Zbl 1133.37025

Summary: In this paper, some existence theorems of periodic solutions of a class of the nonautonomous second order Hamiltonian systems
$\ddot x(t)-B(t)x(t)+\nabla H(t,x(t))=0,\quad t\in [0,T],$
are obtained by a mountain pass theorem and a local link theorem.

### MSC:

 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 34C25 Periodic solutions to ordinary differential equations
Full Text:

### References:

 [1] Bartsch, T.; Willem, M., Periodic solutions of nonautonomous Hamiltonian systems with symmetries, J. reine angew. math., 451, 149-159, (1994) · Zbl 0794.58037 [2] Ding, Y.H., Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems, Nonlinear anal., 25, 1095-1113, (1995) · Zbl 0840.34044 [3] Faraci, F., Multiple periodic solutions for second order systems with changing sign potential, J. math. anal. appl., 319, 567-578, (2006) · Zbl 1099.34040 [4] Fei, G.H., On periodic solutions of superquadratic Hamiltonian systems, J. differential equations, 8, 1-12, (2002) · Zbl 0999.37039 [5] Li, S.J.; Willem, M., Applications of local linking to critical point theory, J. math. anal. appl., 189, 6-32, (1995) · Zbl 0820.58012 [6] Mawhin, J.; Willem, M., Critical point theory and Hamiltonian systems, Appl. math. sci., ISBN: 0-387-96908-X, vol. 74, (1989), Springer New York, xiv+227 pp · Zbl 0676.58017 [7] Ou, Z.Q.; Tang, C.L., Existence of homoclinic solution for the second order Hamiltonian systems, J. math. anal. appl., 291, 203-213, (2004) · Zbl 1057.34038 [8] Rabinowitz, P., Minimax methods in critical point theory with applications to differential equations, CBMS reg. conf., vol. 65, (1986), Amer. Math. Soc. [9] Tang, C.L.; Wu, X.P., Notes on periodic solutions of subquadratic second order systems, J. math. anal. appl., 285, 8-16, (2003) · Zbl 1054.34075 [10] Tao, Z.L.; Tang, C.L., Periodic and subharmonic solutions of second-order Hamiltonian systems, J. math. anal. appl., 293, 435-445, (2004) · Zbl 1042.37047 [11] Wu, X., Saddle point characterization and multiplicity of periodic solutions of non-autonomous second-order systems, Nonlinear anal., 58, 899-907, (2004) · Zbl 1058.34053 [12] Zhao, F.K.; Wu, X., Periodic solutions for a class of non-autonomous second order systems, J. math. anal. appl., 296, 422-434, (2004) · Zbl 1050.34062 [13] Zou, W.M.; Li, S.J., Infinitely many solutions for Hamiltonian systems, J. differential equations, 186, 141-164, (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.