Periodic and subharmonic solutions of second-order Hamiltonian systems. (English) Zbl 1042.37047

Summary: Some solvability conditions of periodic solutions and subharmonic solutions are obtained for a class of new superquadratic non-autonomous second-order Hamiltonian systems by the minimax methods in critical point theory.


37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
49J35 Existence of solutions for minimax problems
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[1] Rabinowitz, P.H., Periodic solutions of Hamiltonian systems, Comm. pure appl. math., 31, 157-184, (1978) · Zbl 0358.70014
[2] Long, Y.M., Multiple solutions of perturbed superquadratic second order Hamiltonian systems, Trans. amer. math. soc., 311, 749-780, (1989) · Zbl 0676.34026
[3] Li, S.; Willem, M., Applications of local linking to critical point theory, J. math. anal. appl., 189, 6-32, (1995) · Zbl 0820.58012
[4] Benci, V., Some critical point theorems and applications, Comm. pure appl. math., 33, 147-172, (1980) · Zbl 0472.58009
[5] Fei, G., On periodic solutions of superquadratic Hamiltonian systems, Electron. J. differential equations, 2002, 1-12, (2002) · Zbl 0999.37039
[6] Rabinowitz, P.H., On subharmonic solutions of superquadratic Hamiltonian systems, Comm. pure appl. math., 33, 609-633, (1980) · Zbl 0425.34024
[7] Benci, V.; Rabinowitz, P.H., Critical point theorems for indefinite functionals, Invent. math., 52, 241-273, (1979) · Zbl 0465.49006
[8] Fonda, A.; Ramos, M., Large-amplitude subharmonic oscillations for scalar second order differential equations with asymmetric nonlinearities, J. differential equations, 109, 354-372, (1994) · Zbl 0798.34048
[9] Liu, J.Q.; Wang, Z.Q., On subharmonics with minimal periods of Hamiltonian systems, Nonlinear anal., 20, 803-821, (1993) · Zbl 0789.58030
[10] Mawhin, J.; Willem, M., Critical point theory and Hamiltonian systems, (1989), Springer-Verlag New York · Zbl 0676.58017
[11] 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
[12] 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
[13] Cerami, G., An existence criterion for the critical points on unbounded manifolds, Istit. lombardo accad. sci. lett. rend. A, 112, 332-336, (1978), (in Italian) · Zbl 0436.58006
[14] Bartolo, P.; Benci, V.; Fortunato, D., Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear anal., 7, 241-273, (1983) · Zbl 0522.58012
[15] Rabinowitz, P.H., Minimax methods in critical point theory with applications to differential equations, CBMS reg. conf. ser. in math., vol. 65, (1986), American Mathematical Society Providence, RI · Zbl 0609.58002
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