- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- 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
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 783509, 9 pages
Upper and Lower Solutions for -Point Impulsive BVP with One-Dimensional -Laplacian
1School of Science, China University of Geosciences, Beijing 100083, China
2College of Science, Hebei University of Engineering, Handan 056038, China
3Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Received 30 July 2013; Revised 13 October 2013; Accepted 15 October 2013
Academic Editor: Gabriele Bonanno
Copyright © 2013 Junfang Zhao 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. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Singapore, 1989.
- D. D. Baĭnov and P. S. Simeonov, Systems with Impulse Effect, Ellis Horwood Series: Mathematics and Its Applications, Ellis Horwood, Chichester, UK, 1989.
- A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, vol. 14 of World Scientific Series on Nonlinear Science: Series A: Monographs and Treatises, World Scientific, Singapore, 1995.
- Z. L. Wei, “Periodic boundary value problems for second order impulsive integrodifferential equations of mixed type in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 195, no. 1, pp. 214–229, 1995.
- S. G. Hristova and D. D. Bainov, “Monotone-iterative techniques of V. Lakshmikantham for a boundary value problem for systems of impulsive differential-difference equations,” Journal of Mathematical Analysis and Applications, vol. 197, no. 1, pp. 1–13, 1996.
- X. Liu and D. Guo, “Periodic boundary value problems for a class of second-order impulsive integro-differential equations in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 216, no. 1, pp. 284–302, 1997.
- R. P. Agarwal and D. O'Regan, “Multiple nonnegative solutions for second order impulsive differential equations,” Applied Mathematics and Computation, vol. 114, no. 1, pp. 51–59, 2000.
- W. Ding and M. Han, “Periodic boundary value problem for the second order impulsive functional differential equations,” Applied Mathematics and Computation, vol. 155, no. 3, pp. 709–726, 2004.
- 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.
- C. D. Coster and P. Habets, Two-Point Boundary Value Problems: Lower and Upper Solutions, Elsevier, New York, NY, USA, 2006.
- D. Jiang, “Upper and lower solutions method and a singular superlinear boundary value problem for the one-dimensional -Laplacian,” Computers & Mathematics with Applications, vol. 42, no. 6-7, pp. 927–940, 2001.
- J. Shen and W. Wang, “Impulsive boundary value problems with nonlinear boundary conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 11, pp. 4055–4062, 2008.
- I. Rachůnková and J. Tomeček, “Impulsive BVPs with nonlinear boundary conditions for the second order differential equations without growth restrictions,” Journal of Mathematical Analysis and Applications, vol. 292, no. 2, pp. 525–539, 2004.
- D. Jiang, “Upper and lower solutions method and a superlinear singular boundary value problem,” Computers & Mathematics with Applications, vol. 44, no. 3-4, pp. 323–337, 2002.
- A. Cabada and R. L. Pouso, “Existence results for the problem with nonlinear boundary conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 35, no. 2, pp. 221–231, 1999.
- H. Lü, D. O'Regan, and R. P. Agarwal, “Triple solutions for the one-dimensional -Laplacian,” Glasnik Matematički, vol. 38, no. 2, pp. 273–284, 2003.
- M. X. Wang, A. Cabada, and J. J. Nieto, “Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions,” Annales Polonici Mathematici, vol. 58, no. 3, pp. 221–235, 1993.