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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 134691, 9 pages
Existence Result for Impulsive Differential Equations with Integral Boundary Conditions
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Received 5 December 2012; Accepted 5 January 2013
Academic Editor: Yonghui Xia
Copyright © 2013 Peipei Ning 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.
- V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific Publishing, Singapore, 1989.
- D. Bainov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK, 1993.
- D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, San Diego, Calif, USA, 1988.
- D. Guo, J. Sun, and Z. Liu, Nonlinear Ordinary Differential Equations Functional Technologies, Shan Dong Science Technology, 1995.
- A. Boucherif, “Second-order boundary value problems with integral boundary conditions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 1, pp. 364–371, 2009.
- G. Infante, “Eigenvalues and positive solutions of ODEs involving integral boundary conditions,” Discrete and Continuous Dynamical Systems A, vol. 2005, supplement, pp. 436–442, 2005.
- W. Ding and Y. Wang, “New result for a class of impulsive differential equation with integral boundary conditions,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 5, pp. 1095–1105, 2013.
- D. Guo, “Second order impulsive integro-differential equations on unbounded domains in Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 35, no. 4, pp. 413–423, 1999.
- T. He, F. Yang, C. Chen, and S. Peng, “Existence and multiplicity of positive solutions for nonlinear boundary value problems with a parameter,” Computers & Mathematics with Applications, vol. 61, no. 11, pp. 3355–3363, 2011.
- X. Hao, L. Liu, and Y. Wu, “Existence and multiplicity results for nonlinear periodic boundary value problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 9-10, pp. 3635–3642, 2010.
- Z. Yang, “Positive solutions of a second-order integral boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 321, no. 2, pp. 751–765, 2006.
- F. M. Atici and G. S. Guseinov, “On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions,” Journal of Computational and Applied Mathematics, vol. 132, no. 2, pp. 341–356, 2001.
- R. Liang and J. Shen, “Eigenvalue criteria for existence of positive solutions of impulsive differential equations with non-separated boundary conditions,” submitted.