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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 401740, 11 pages
Existence and Multiplicity of Solutions to a Boundary Value Problem for Impulsive Differential Equations
1Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
2School of Mathematics and Computer Science, Panzhihua University, Panzhihua, Sichuan 617000, China
Received 24 October 2012; Revised 20 December 2012; Accepted 21 December 2012
Academic Editor: Wan-Tong Li
Copyright © 2013 Chunyan He 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.
- M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2 of Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, NY, USA, 2006.
- A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing, River Edge, NJ, USA, 1995.
- J. J. Nieto and R. Rodríguez-López, “Boundary value problems for a class of impulsive functional equations,” Computers & Mathematics with Applications, vol. 55, no. 12, pp. 2715–2731, 2008.
- W. M. Haddad, V. Chellaboina, and S. G. Nersesov, Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, USA, 2006.
- Z. Luo and J. J. Nieto, “New results for the periodic boundary value problem for impulsive integro-differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 6, pp. 2248–2260, 2009.
- J. Chu and J. J. Nieto, “Impulsive periodic solutions of first-order singular differential equations,” Bulletin of the London Mathematical Society, vol. 40, no. 1, pp. 143–150, 2008.
- E. K. Lee and Y.-H. Lee, “Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations,” Applied Mathematics and Computation, vol. 158, no. 3, pp. 745–759, 2004.
- M. Yao, A. Zhao, and J. Yan, “Periodic boundary value problems of second-order impulsive differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 1, pp. 262–273, 2009.
- X. Lin and D. Jiang, “Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations,” Journal of Mathematical Analysis and Applications, vol. 321, no. 2, pp. 501–514, 2006.
- Y. Tian and W. Ge, “Multiple positive solutions for a second order Sturm-Liouville boundary value problem with a -Laplacian via variational methods,” The Rocky Mountain Journal of Mathematics, vol. 39, no. 1, pp. 325–342, 2009.
- 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.
- J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, vol. 74 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989.
- S. Luan and A. Mao, “Periodic solutions for a class of non-autonomous Hamiltonian systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 61, no. 8, pp. 1413–1426, 2005.
- P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol. 65 of CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, USA, 1986.
- K. Teng and C. Zhang, “Existence of solution to boundary value problem for impulsive differential equations,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4431–4441, 2010.
- 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.
- Y. Tian and W. Ge, “Applications of variational methods to boundary-value problem for impulsive differential equations,” Proceedings of the Edinburgh Mathematical Society. Series II, vol. 51, no. 2, pp. 509–527, 2008.
- L. Bai and B. Dai, “Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory,” Mathematical and Computer Modelling, vol. 53, no. 9-10, pp. 1844–1855, 2011.
- M. del Pino, M. Elgueta, and R. Manásevich, “A homotopic deformation along of a Leray-Schauder degree result and existence for , ,” Journal of Differential Equations, vol. 80, no. 1, pp. 1–13, 1989.
- W. D. Lu, Variational Methods in Differential Equations, Scientific Publishing House, Beijing, China, 2002.
- P. Lindqvist, “On the equation div,” Proceedings of the American Mathematical Society, vol. 109, no. 1, pp. 157–164, 1990.