On periodic solutions of subquadratic second order non-autonomous Hamiltonian systems. (English) Zbl 1319.34071

Summary: We are concerned with the existence of periodic solutions for second order non-autonomous Hamiltonian systems under a new subquadratic growth condition. By using the minimax methods in critical point theory, an existence theorem is obtained, which extends and improves some known results in the literature.


34C25 Periodic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
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[1] 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
[2] Tang, C. L.; Wu, X. P., Periodic solutions for a class of new superquadratic second order Hamiltonian systems, Appl. Math. Lett., 34, 65-71, (2014) · Zbl 1314.34090
[3] Ekeland, I.; Ghoussoub, N., Certain new aspects of the calculus of variations in the large, Bull. Amer. Math. Soc., 39, 207-265, (2002) · Zbl 1064.35054
[4] Mawhin, J.; Wliiem, M., Critical point theory and Hamiltonian systems, (1989), Springer-Verlag New York
[5] Pipan, J.; Schechter, M., Non-autonomous second order Hamiltonian systems, J. Differential Equations, 257, 351-373, (2014) · Zbl 1331.37085
[6] Schechter, M., Periodic nonautonomous second order dynamical systems, J. Differential Equations, 223, 290-302, (2006) · Zbl 1099.34042
[7] Rabinowitz, P., On subharmonic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 33, 609-633, (1980) · Zbl 0425.34024
[8] Bartolo, P.; Benci, V.; Fortunato, D., Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Anal., 7, 981-1012, (1983) · Zbl 0522.58012
[9] Rabinowitz, P., Minimax methods in critical point theory with applications to differential equations, (CBMS Reg. Conf. Ser. Math., vol. 65, (1986), Amer. Math. Soc Providence. RI)
[10] Jiang, Q.; Tang, C. L., Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems, J. Math. Anal. Appl., 328, 380-389, (2007) · Zbl 1118.34038
[11] Ma, S.; Zhang, Y., Existence of infinitely many periodic solutions for ordinary \(p\)-Laplacian systems, J. Math. Anal. Appl., 351, 469-479, (2009) · Zbl 1153.37009
[12] Zou, W., Multiple solutions for second-order Hamiltonian systems via computation of the critical groups, Nonlinear Anal., 44, 975-989, (2001) · Zbl 0997.37039
[13] Tang, X. H.; Jiang, J., Existence and multiplicity of periodic solutions for a class of second-order Hamiltonian systems, Comput. Math. Appl., 59, 3646-3655, (2010) · Zbl 1206.34059
[14] Wang, Z.; Zhang, J., Periodic solutions of a class of second order non-autonomous Hamiltonian systems, Nonlinear Anal., 72, 4480-4487, (2010) · Zbl 1206.34060
[15] Wang, Z.; Zhang, J.; Zhang, Z., Periodic solutions of second order non-autonomous Hamiltonian systems with local superquadratic potential, Nonlinear Anal., 70, 3672-3681, (2009) · Zbl 1179.34037
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