Abstract
In this paper, we investigate the periodic solutions for a class of non-autonomous Hamiltonian systems. By using a decomposition technique of space and variational approaches we give new sufficient conditions for the existence of multiple periodic solutions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Brezis, L. Nirenberg. Remarks on finding critical points, Commun. Pure Appl. math. 44 (1991), 939–963.
Guo Dajun. Nonlinear Functional Analysis, Shandong science and technology Press, Shandong, China 1985.
J. Mawhin, M. Willem. Critical Point Theory and Hamiltonian Systems, Springer-Verlag, Berlin 1989.
J. J. Nieto, D. O’Regan. Variational approach to impulsive differential equations, Nonlinear Anal.: Real World Applications 10 (2009), 680–690.
P. H. Rabinowitz. Minimax Methods in Critical Point Theory with Applicatins to Differential Equations, CBMS Regional Conf. Ser. in Math., 65, American Mathematical Society, Providence, RI 1986.
B. Ricceri. On a three critical points theorem, Arch. Math. (Basel) 75 (2000), 220–226.
B. Ricceri. A general multiplicity theorem for certain nonlinear equations in Hilbert spaces, Proc. Amer. Math. Soc. 133 (2005), 3255–3261.
C. Tang. Periodic solutions of non-autonomous second order systems with γ-quasisubadditive potential, J. Math. Anal. Appl. 189 (1995), 671–675.
C. Tang. Existence and multiplicity of periodic solutions for nonautonomous second order systems, Nonlinear Anal. TMA 32(3) (1998), 299–304.
C. Tang. Periodic solutions of non-autonomous second order systems, J. Math. Anal. Appl. 202 (1996), 465–469.
C. Tang, X. Wu. Periodic solutions for second order systems with sublinear nonlinearity, Proc. Amer. Math. Soc. 126(11) (1998), 3263–3270.
C. Tang, X. Wu. Periodic solutions for a class of nonautonomous subquadratic second order Hamiltonian systems, J. Math. Anal. Appl. 275 (2002), 870–882.
Y. Tian, W. G. Ge. Periodic solutions of non-autonomous second-order systems with a p-Laplacian, Nonlinear Anal. 66 (2007), 192–203.
Y. Tian, W. G. Ge. Multiple positive solutions for a second-order Sturm-Liouville boundary value problem with a p-Laplacian via variational methods, Rocky Mountain J. Math. 39(1) 2009, 325–342.
Y. Tian, W. G. Ge. Applications of Variational Methods to Boundary Value Problem for Impulsive Differential Equations, Proceedings of Edinburgh Mathematical Society 51 (2008) 509–527.
Q. Wang, Z. Wang, J. Shi. Subharmonic oscillations with prescribed minimal period for a class of Hamiltonian systems, Nonlinear Anal. 28 (1996), 1273–1282.
X. Wu, C. Tang. Periodic solutions of nonautonomous second-order Hamiltonian systems with even-typed potentials, Nonlinear Anal. 55 (2003), 759–769.
J. Yu, Subharmonic solutions with prescribed minimal period of a class of nonautonomous Hamiltonian systems, J. Dyn. Diff. Equat. 20 (2008), 787–796.
E. Zeidler. Nonlinear Functional Analysis and its Applications, III Springer, 1985.
J. Zhou, Y. Li. Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects, Nonlinear Anal. 71 (2009), 2856–2865.
J. Zhou, Y. Li. Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects, Nonlinear Anal. 72 (2010), 1594–1603.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project 11001028 Supported by National Science Foundation for Young Scholars, Project 11071014 Supported by National Science Foundation of P.R. China.
Rights and permissions
About this article
Cite this article
Tian, Y., Ge, W. Multiple periodic solutions for a class of non-autonomous hamiltonian systems with even-typed potentials. J Dyn Control Syst 18, 339–354 (2012). https://doi.org/10.1007/s10883-012-9147-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10883-012-9147-2