- 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 2013 (2013), Article ID 908062, 10 pages
Existence of Solution for Impulsive Differential Equations with Nonlinear Derivative Dependence via Variational Methods
1Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China
2Hunan Normal University Press, Changsha, Hunan 410081, China
3School of Economics and Management, Changsha University of Science and Technology, Changsha, Hunan 410004, China
Received 30 May 2013; Revised 1 August 2013; Accepted 22 August 2013
Academic Editor: M. Victoria Otero-Espinar
Copyright © 2013 Lizhao Yan 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.
- G. Zeng, F. Wang, and J. J. Nieto, “Complexity of a delayed predator-prey model with impulsive harvest and Holling type II functional response,” Advances in Complex Systems, vol. 11, no. 1, pp. 77–97, 2008.
- R. K. George, A. K. Nandakumaran, and A. Arapostathis, “A note on controllability of impulsive systems,” Journal of Mathematical Analysis and Applications, vol. 241, no. 2, pp. 276–283, 2000.
- G. Jiang, Q. Lu, and L. Qian, “Complex dynamics of a Holling type II prey-predator system with state feedback control,” Chaos, Solitons & Fractals, vol. 31, no. 2, pp. 448–461, 2007.
- G. Jiang, Q. Lu, and L. Qian, “Chaos and its control in an impulsive differential system,” Chaos, Solitons & Fractals, vol. 34, no. 4, pp. 1135–1147, 2007.
- J. Jiao, X. Yang, L. Chen, and S. Cai, “Effect of delayed response in growth on the dynamics of a chemostat model with impulsive input,” Chaos, Solitons & Fractals, vol. 42, no. 4, pp. 2280–2287, 2009.
- S. I. Nenov, “Impulsive controllability and optimization problems in population dynamics,” Nonlinear Analysis. Theory, Methods & Applications, vol. 36, no. 7, pp. 881–890, 1999.
- S. Tang and L. Chen, “Density-dependent birth rate, birth pulses and their population dynamic consequences,” Journal of Mathematical Biology, vol. 44, no. 2, pp. 185–199, 2002.
- M. Choisy, J.-F. Guégan, and P. Rohani, “Dynamics of infectious diseases and pulse vaccination: teasing apart the embedded resonance effects,” Physica D, vol. 223, no. 1, pp. 26–35, 2006.
- S. Gao, L. Chen, J. J. Nieto, and A. Torres, “Analysis of a delayed epidemic model with pulse vaccination and saturation incidence,” Vaccine, vol. 24, pp. 6037–6045, 2006.
- G.-l. Cai and W.-G. Ge, “Positive solutions for second order impulsive differential equations with dependence on first order derivative,” Journal of Mathematical Research and Exposition, vol. 26, no. 4, pp. 725–734, 2006.
- D. J. Guo and J. X. Sun, Functional Methods of Ordinary Differential Equation, Shandong Science Technology Press, Jinan, China, 1995.
- Y. P. Guo and W. G. Ge, “Positive solutions for three-point boundary value problems with dependence on the first order derivative,” Journal of Mathematical Analysis and Applications, vol. 290, no. 1, pp. 291–301, 2004.
- J. H. Shen and W. B. Wang, “Impulsive boundary value problems with nonlinear boundary conditions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 11, pp. 4055–4062, 2008.
- Y. Zhao and H. Chen, “Multiplicity of solutions to two-point boundary value problems for second-order impulsive differential equations,” Applied Mathematics and Computation, vol. 206, no. 2, pp. 925–931, 2008.
- D. De Figueiredo, M. Girardi, and M. Matzeu, “Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques,” Differential and Integral Equations, vol. 17, no. 1-2, pp. 119–126, 2004.
- 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.
- J. J. Nieto, “Variational formulation of a damped Dirichlet impulsive problem,” Applied Mathematics Letters, vol. 23, no. 8, pp. 940–942, 2010.
- J. Xiao, J. J. Nieto, and Z. Luo, “Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 426–432, 2012.
- Y. Tian and W. Ge, “Applications of variational methods to boundary-value problem for impulsive differential equations,” Proceedings of the Edinburgh Mathematical Society, vol. 51, no. 2, pp. 509–527, 2008.
- J. Sun and H. Chen, “Variational method to the impulsive equation with Neumann boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 316812, 17 pages, 2009.
- 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.
- 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.
- P. Chen and X. Tang, “Existence and multiplicity of solutions for second-order impulsive differential equations with Dirichlet problems,” Applied Mathematics and Computation, vol. 218, no. 24, pp. 11775–11789, 2012.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific Publishing Co. Inc., Singapore, 1989.
- P. Lindqvist, “On the equation ,” Proceedings of the American Mathematical Society, vol. 109, no. 1, pp. 157–164, 1990.