Abstract
This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.
Similar content being viewed by others
References
Ladde G. S., Lakshmikantham V., Vatsala A. S., Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, London, 1985
Ladde G. S., Sathanantham S., Periodic boundary value problem for impulsive integrodifferential equations of Volterra type, J. Math. Phy. Sci., 1991, 25:119–129
Liu X. Z., Iterative methods for solutions of impulsive functional differential systems, Appl. Anal., 1992, 44:171–182
Guo D. J., Lakshmikantham V., Liu X. Z., Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers, Dordrecht, 1996
Hristova G. S., Bainov D. D., Monotone iterative techniques of V. Lakshmikantham for a boundary value problem for systems of impulsive differential-difference equations, J. Math. Anal. Appl., 1996, 197:1–13
Hristova G. S., Bainov D. D., Application of the monotone iterative-techniques of Lakshmikantham V. for solving the initial value problem for impulsive differential-difference equations, J. Rocky. Mountain Math., 1993, 23:609–618
Leela S., Oğuztöreli M N. Periodic boundary value problem for differential equations with delay and monotone iterative method, J. Math. Anal. Appl., 1987, 122:301–307
Liz E. Periodic boundary value problems for a calass of functional differential equations, J. Math. Anal. Appl., 1996, 200:680–686
Lakshmikantham V., BainovD. D., Simeonov P. S., Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989
Bainov D. D., Simenov P. S., Impulsive Differential Equations:Periodic Solutions and Applications, Longman: Harlow, 1993
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, Z.M., Ge, W.G. The Monotone Iterative Technique and Periodic Boundary Value Problem for First Order Impulsive Functional Differential Equations. Acta Math Sinica 18, 253–262 (2002). https://doi.org/10.1007/s101140200155
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s101140200155
Keywords
- Impulsive functional differential equation
- Upper and lower solution
- Monotone iterative technique
- Periodic boundary value problem