×

Periodic solutions for a class of superquadratic Hamiltonian systems. (English) Zbl 1123.34311

The existence of nontrivial critical points for a class of superquadratic nonautonomous second order Hamiltonian systems is considered. Some new results on the existence of nontrivial periodic solutions are obtained.

MSC:

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

References:

[1] Rabinowitz, P.H., Periodic solutions of Hamiltonian systems, Comm. pure appl. math., 31, 157-184, (1978) · Zbl 0358.70014
[2] Li, Shujie; Willem, Michel, Applications of local linking to critical point theory, J. math. anal. appl., 189, 6-32, (1995) · Zbl 0820.58012
[3] Long, Y.M., Multiple solutions of perturbed superquadratic second order Hamiltonian systems, Trans. amer. math. soc., 311, 749-780, (1987) · Zbl 0676.34026
[4] Tao, Zhu-Lian; Tang, Chun-lei, Periodic and subharmonic solutions of second-order Hamiltonian systems, J. math. anal. appl., 293, 435-445, (2004) · Zbl 1042.37047
[5] Luan, Shixia; Mao, Anmin, Periodic solutions for a class of non-autonomous Hamiltonian systems, Nonlinear anal., 61, 1413-1426, (2005) · Zbl 1071.34039
[6] Fei, G., On periodic solutions of superquadratic Hamiltonian systems, Electron. J. differential equations, 08, 1-12, (2002) · Zbl 0999.37039
[7] Benci, V., Some critical point theorems and applications, Comm. pure appl. math., 33, 147-172, (1980) · Zbl 0472.58009
[8] Mawhin, J.; Willem, M., Critical point theory and Hamiltonian systems, (1989), Springer-Verlag New York · Zbl 0676.58017
[9] Rabinowitz, P.H., Minimax methods in critical point theory with applications to differential equations, CBMS reg. conf. ser. math., vol. 65, (1986), Amer. Math. Soc. Providence, RI · Zbl 0609.58002
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.