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Multiplicity of subharmonic solutions and periodic solutions of a particular type of super-quadratic Hamiltonian systems
1. | Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China, China |
References:
[1] |
T. Q. An and Z. Q. Wang, Periodic solutions of Hamiltonian systems with anisotropic growth, Comm. Pure Appl. Ana., 9 (2010), 1069-1082.
doi: 10.3934/cpaa.2010.9.1069. |
[2] |
S. L. Chen and C. H. Tang, Periodic and subharmonic solutions of a class of superquadratic Hamiltonian systems, J. Math. Anal. Appl., 297 (2004), 267-284.
doi: 10.1016/j.jmaa.2004.05.006. |
[3] |
G. H. Fei, On periodic solutions of superquadratic Hamiltonian systems, Electro. J. Differential Equations, 8 (2002), 1-12. |
[4] |
P. L. Felmer, Periodic solutions of "superquadratic'' Hamiltonian systems, J. Differential Equations, 102 (1993), 188-207.
doi: 10.1006/jdeq.1993.1027. |
[5] |
P. L. Felmer and Z. Q. Wang, Multiplicity for symmetric indefinite functionals: applications to Hamiltonian systems and elliptic systems, Topol. Methods Nonlinear Anal., 12 (1998), 207-226. |
[6] |
C. Li and C. G. Liu, Brake subharmonic solutions of first order Hamiltonian systems, Sci. China Math., 53 (2010), 2719-2732.
doi: 10.1007/s11425-010-4105-5. |
[7] |
C. G. Liu, Subharmonic solutions of Hamiltonian systems, Nonlinear Anal., 42 (2000), 185-198.
doi: 10.1016/S0362-546X(98)00339-3. |
[8] |
Y. Long, Periodic solutions of perturbed super-quadratic Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa. Serie IV. Vol. XVII. Fasc., 1 (1990), 35-77. |
[9] |
Y. Long, Periodic solutions of Hamiltonian systems with bounded forcing terms, Math. Z., 203 (1990), 453-467.
doi: 10.1007/BF02570749. |
[10] |
J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York, 1989.
doi: 10.1007/978-1-4757-2061-7. |
[11] |
P. H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), 157-184. |
[12] |
P. H. Rabinowitz, On subhamonic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 33 (1980), 609-633.
doi: 10.1002/cpa.3160330504. |
[13] |
P. H. Rabinowitz, Periodic solutions of large norm of Hamiltonian systems, J. Differential Equations, 50 (1986), 33-48.
doi: 10.1016/0022-0396(83)90083-9. |
[14] |
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math. 65, American Mathematical Society, Providence, 1986.
doi: 10.1090/cbms/065. |
[15] |
C. H. Tang, Existence and multiplicity of periodic solutions for nonautonomous second order systems, Nonlinear Anal., 32 (1998), 299-304.
doi: 10.1016/S0362-546X(97)00493-8. |
[16] |
X. J. Xu, Periodic solutions for non-autonomous Hamiltonian systems possessing super-quardratic potentials, Nonlinear Anal., 51 (2002), 941-955.
doi: 10.1016/S0362-546X(01)00870-7. |
[17] |
Q. Y. Zhang and C. G. Liu, Infinitely many periodic solutions for second order Hamiltonian systems, J. Differential Equations, 251 (2011), 816-833.
doi: 10.1016/j.jde.2011.05.021. |
[18] |
X. F. Zhang and F. Guo, Existence of periodic solutions of a particular type of super-quadratic Hamiltonian systems, J. Math. Anal. Appl., 421 (2015), 1587-1602.
doi: 10.1016/j.jmaa.2014.08.006. |
[19] |
W. Zou and S. Li, Infinitely many solutions for Hamiltonian systems, J. Differential Equations, 186 (2002), 141-164.
doi: 10.1016/S0022-0396(02)00005-0. |
show all references
References:
[1] |
T. Q. An and Z. Q. Wang, Periodic solutions of Hamiltonian systems with anisotropic growth, Comm. Pure Appl. Ana., 9 (2010), 1069-1082.
doi: 10.3934/cpaa.2010.9.1069. |
[2] |
S. L. Chen and C. H. Tang, Periodic and subharmonic solutions of a class of superquadratic Hamiltonian systems, J. Math. Anal. Appl., 297 (2004), 267-284.
doi: 10.1016/j.jmaa.2004.05.006. |
[3] |
G. H. Fei, On periodic solutions of superquadratic Hamiltonian systems, Electro. J. Differential Equations, 8 (2002), 1-12. |
[4] |
P. L. Felmer, Periodic solutions of "superquadratic'' Hamiltonian systems, J. Differential Equations, 102 (1993), 188-207.
doi: 10.1006/jdeq.1993.1027. |
[5] |
P. L. Felmer and Z. Q. Wang, Multiplicity for symmetric indefinite functionals: applications to Hamiltonian systems and elliptic systems, Topol. Methods Nonlinear Anal., 12 (1998), 207-226. |
[6] |
C. Li and C. G. Liu, Brake subharmonic solutions of first order Hamiltonian systems, Sci. China Math., 53 (2010), 2719-2732.
doi: 10.1007/s11425-010-4105-5. |
[7] |
C. G. Liu, Subharmonic solutions of Hamiltonian systems, Nonlinear Anal., 42 (2000), 185-198.
doi: 10.1016/S0362-546X(98)00339-3. |
[8] |
Y. Long, Periodic solutions of perturbed super-quadratic Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa. Serie IV. Vol. XVII. Fasc., 1 (1990), 35-77. |
[9] |
Y. Long, Periodic solutions of Hamiltonian systems with bounded forcing terms, Math. Z., 203 (1990), 453-467.
doi: 10.1007/BF02570749. |
[10] |
J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York, 1989.
doi: 10.1007/978-1-4757-2061-7. |
[11] |
P. H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), 157-184. |
[12] |
P. H. Rabinowitz, On subhamonic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 33 (1980), 609-633.
doi: 10.1002/cpa.3160330504. |
[13] |
P. H. Rabinowitz, Periodic solutions of large norm of Hamiltonian systems, J. Differential Equations, 50 (1986), 33-48.
doi: 10.1016/0022-0396(83)90083-9. |
[14] |
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math. 65, American Mathematical Society, Providence, 1986.
doi: 10.1090/cbms/065. |
[15] |
C. H. Tang, Existence and multiplicity of periodic solutions for nonautonomous second order systems, Nonlinear Anal., 32 (1998), 299-304.
doi: 10.1016/S0362-546X(97)00493-8. |
[16] |
X. J. Xu, Periodic solutions for non-autonomous Hamiltonian systems possessing super-quardratic potentials, Nonlinear Anal., 51 (2002), 941-955.
doi: 10.1016/S0362-546X(01)00870-7. |
[17] |
Q. Y. Zhang and C. G. Liu, Infinitely many periodic solutions for second order Hamiltonian systems, J. Differential Equations, 251 (2011), 816-833.
doi: 10.1016/j.jde.2011.05.021. |
[18] |
X. F. Zhang and F. Guo, Existence of periodic solutions of a particular type of super-quadratic Hamiltonian systems, J. Math. Anal. Appl., 421 (2015), 1587-1602.
doi: 10.1016/j.jmaa.2014.08.006. |
[19] |
W. Zou and S. Li, Infinitely many solutions for Hamiltonian systems, J. Differential Equations, 186 (2002), 141-164.
doi: 10.1016/S0022-0396(02)00005-0. |
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