Journal Menu
- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 616427, 8 pages
doi:10.1155/2012/616427
Research Article
Periodic Solutions of Some Impulsive Hamiltonian Systems with Convexity Potentials
School of Mathematical Sciences and Computing Technology, Central South University, Hunan, Changsha 410083, China
Received 31 August 2012; Accepted 18 November 2012
Academic Editor: Juntao Sun
Copyright © 2012 Dezhu Chen and Binxiang Dai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, vol. 74, Springer, Berlin, Germany, 1989. View at Zentralblatt MATH
- C.-L. Tang and X.-P. Wu, “Some critical point theorems and their applications to periodic solution for second order Hamiltonian systems,” Journal of Differential Equations, vol. 248, no. 4, pp. 660–692, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Mawhin, “Semicoercive monotone variational problems,” Académie Royale de Belgique, Bulletin de la Classe des Sciences, vol. 73, no. 3-4, pp. 118–130, 1987.
- C.-L. Tang, “An existence theorem of solutions of semilinear equations in reflexive Banach spaces and its applications,” Académie Royale de Belgique, Bulletin de la Classe des Sciences, vol. 4, no. 7–12, pp. 317–330, 1996. View at Zentralblatt MATH
- J. J. Nieto, “Variational formulation of a damped Dirichlet impulsive problem,” Applied Mathematics Letters, vol. 23, no. 8, pp. 940–942, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. J. Nieto and D. O'Regan, “Variational approach to impulsive differential equations,” Nonlinear Analysis. Real World Applications, vol. 10, no. 2, pp. 680–690, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Zhou and Y. Li, “Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1594–1603, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- H. Zhang and Z. Li, “Periodic solutions of second-order nonautonomous impulsive di erential equations,” International Journal of Qualitative Theory of Differential Equations and Applications, vol. 2, no. 1, pp. 112–124, 2008.
- J. Zhou and Y. Li, “Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2856–2865, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- W. Ding and D. Qian, “Periodic solutions for sublinear systems via variational approach,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 2603–2609, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- H. Zhang and Z. Li, “Periodic and homoclinic solutions generated by impulses,” Nonlinear Analysis: Real World Applications, vol. 12, no. 1, pp. 39–51, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Z. Zhang and R. Yuan, “An application of variational methods to Dirichlet boundary value problem with impulses,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 155–162, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- D. Zhang and B. Dai, “Infinitely many solutions for a class of nonlinear impulsive differential equations with periodic boundary conditions,” Computers & Mathematics with Applications, vol. 61, no. 10, pp. 3153–3160, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- L. Yang and H. Chen, “Existence and multiplicity of periodic solutions generated by impulses,” Abstract and Applied Analysis, vol. 2011, Article ID 310957, 15 pages, 2011. View at Publisher · View at Google Scholar
- J. Sun, H. Chen, and J. J. Nieto, “Infinitely many solutions for second-order Hamiltonian system with impulsive effects,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 544–555, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Sun, H. Chen, J. J. Nieto, and M. Otero-Novoa, “The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 12, pp. 4575–4586, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH