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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 829052, 8 pages
Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems
1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Department of Mathematics, College of Science, Hohai University, Nanjing 210098, China
3School of ELectrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
Received 3 December 2013; Accepted 10 January 2014; Published 19 February 2014
Academic Editor: Jifeng Chu
Copyright © 2014 Ziheng Zhang et al. 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.
- A. Ambrosetti and V. C. Zelati, Periodic Solutions of Singular Lagrangian Systems, vol. 10 of Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser, Boston, Mass, USA, 1993.
- W. B. Gordon, “Conservative dynamical systems involving strong force,” Transactions of the American Mathematical Society, vol. 204, pp. 113–115, 1975.
- P. H. Rabinowitz, “Periodic solutions of Hamiltonian systems,” Communications on Pure and Applied Mathematics, vol. 31, no. 2, pp. 157–184, 1978.
- K. Tanaka, “Homoclinic orbits for a singular second order Hamiltonian system,” Annales de l'Institut Henri Poincaré C, vol. 7, pp. 427–438, 1990.
- A. Bahri and P. H. Rabinowitz, “A minimax method for a class of Hamiltonian systems with singular potentials,” Journal of Functional Analysis, vol. 82, no. 2, pp. 412–428, 1989.
- P. Caldiroli, “Existence and multiplicity of homoclinic orbits for potentials on unbounded domains,” Proceedings of the Royal Society of Edinburgh A, vol. 124, no. 2, pp. 317–339, 1994.
- U. Bessi, “Multiple homoclinic orbits for autonomous singular potentials,” Proceedings of the Royal Society of Edinburgh A, vol. 124, no. 4, pp. 785–802, 1994.
- J. Janczewska and J. Maksymiuk, “Homoclinic orbits for a class of singular second order Hamiltonian systems in ,” Central European Journal of Mathematics, vol. 10, no. 6, pp. 1920–1927, 2012.
- M. L. Bertotti and L. Jeanjean, “Multiplicity of homoclinic solutions for singular second-order conservative systems,” Proceedings of the Royal Society of Edinburgh A, vol. 126, no. 6, pp. 1169–1180, 1996.
- P. Caldiroli and C. de Coster, “Multiple homoclinics for a class of singular Hamiltonian systems,” Journal of Mathematical Analysis and Applications, vol. 211, no. 2, pp. 556–573, 1997.
- P. H. Rabinowitz, “Homoclinics for a singular Hamiltonian system,” in Geometric Analysis and the Calculus of Variations, pp. 267–296, International Press, Cambridge, Mass, USA, 1996.
- P. Caldiroli and L. Jeanjean, “Homoclinics and heteroclinics for a class of conservative singular hamiltonian systems,” Journal of Differential Equations, vol. 136, no. 1, pp. 76–114, 1997.
- M. J. Borges, “Heteroclinic and homoclinic solutions for a singular Hamiltonian system,” European Journal of Applied Mathematics, vol. 17, no. 1, pp. 1–32, 2006.
- M. Izydorek and J. Janczewska, “The shadowing chain lemma for singular Hamiltonian systems involving strong forces,” Central European Journal of Mathematics, vol. 10, no. 6, pp. 1928–1939, 2012.
- E. Séré, “Existence of infinitely many homoclinic orbits in Hamiltonian systems,” Mathematische Zeitschrift, vol. 209, no. 1, pp. 27–42, 1992.
- E. Sere, “Looking for the Bernoulli shift,” Annales de l'Institut Henri Poincaré C, vol. 10, pp. 561–590, 1993.
- P. Caldiroli and P. Montecchiari, “Homoclinic orbits for second order Hamiltonian systems with potential changing sign,” Communications on Applied Nonlinear Analysis, vol. 1, pp. 97–129, 1994.
- V. C. Zelati and P. H. Rabinowitz, “Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials,” Journal of the American Mathematical Society, vol. 4, no. 4, pp. 693–727, 1991.
- P. H. Rabinowitz, “Multibump solutions for an almost periodically forced singular Hamiltonian system,” Electronic Journal of Differential Equations, vol. 1995, no. 12, pp. 1–21, 1995.
- M. Izydorek and J. Janczewska, “Connecting orbits for a periodically forced singular planar Newtonian system,” Journal of Fixed Point Theory and Applications, vol. 12, no. 1-2, pp. 59–67, 2012.
- D. G. Costa and H. Tehrani, “On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions,” Journal of Mathematical Analysis and Applications, vol. 412, no. 1, pp. 200–211, 2014.
- C. Greco, “Periodic solutions of a class of singular Hamiltonian systems,” Nonlinear Analysis, vol. 12, no. 3, pp. 259–269, 1988.
- P. H. Rabinowitz, “Periodic and heteroclinic orbits for a periodic Hamiltonian system,” Annales de l'Institut Henri Poincaré C, vol. 6, pp. 331–346, 1989.