Solution bundle for a class of impulsive differential inclusions on Banach spaces. (English) Zbl 1113.34046

The paper deals with the existence of a solution bundle for a class of impulsive differential inclusions in Banach spaces. Also a nonlinear semigroup is constructed on nonempty closed bounded subsets of the Banach space to describe the evolution of the set of attainable states.


34G25 Evolution inclusions
34A37 Ordinary differential equations with impulses
Full Text: DOI


[1] Ahmed, N. U., Semigroup Theory with Applications to Systems and Control, Pitman Res. Notes Math. Ser. (1991), Longman Scientific and Technical/John Wiley: Longman Scientific and Technical/John Wiley UK/New York, USA · Zbl 0727.47026
[2] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer-Verlag: Springer-Verlag New York · Zbl 0516.47023
[3] Li, Xunjing; Yong, Jiongmin, Optimal Control Theory for Infinite Dimensional Systems (1995), Birkhäuser: Birkhäuser Boston · Zbl 0817.49001
[4] Lakshmikantham, V.; Bainov, D. D.; Simenov, P. S., Theory of Impulsive Differential Equations (1999), World Scientific: World Scientific Singapore
[5] Pandit, S. G.; Deo, S. G., Differential Systems Involving Impulsive, Lecture Notes in Math., vol. 954 (1982), Springer-Verlag: Springer-Verlag Berlin · Zbl 0417.34085
[6] Ahmed, N. U., Some remarks on the dynamics of impulsive systems in Banach spaces, Dyn. Contin. Discrete Impuls. Syst., 8, 261-274 (2001) · Zbl 0995.34050
[7] Ahmed, N. U., State dependent vector measures as feedback controls for impulsive systems in Banach spaces, Dyn. Contin. Discrete Impuls. Syst., 8, 251-261 (2001) · Zbl 0990.34056
[8] Liu, J. H., Nonlinear impulsive evolution equations, Dyn. Contin. Discrete Impuls. Syst., 6, 1, 77-85 (1999) · Zbl 0932.34067
[9] Guo, D.; Liu, X. I., First order integro-differential equations on unbounded domain in a Banach space, Dyn. Contin. Discrete Impuls. Syst., 2, 3, 77-88 (1996)
[10] Rogovchenko, Y. V., Impulsive evolution systems: Main results and new trends, Dyn. Contin. Discrete Impuls. Syst., 3, 1, 77-88 (1997) · Zbl 0879.34014
[11] Yu, Xiulan; Jiang, Yang, Impulsive perturbation of \(C_0\)-semigroups and a class of semilinear impulsive evolution equation, J. Guizhou University, 20, 4, 350-357 (2003)
[12] Ahmed, N. U., Impulsive perturbation of \(C_0\)-semigroups and evolution inclusions, Nonlinear Funct. Anal. Appl., 9, 1, 127-147 (2004) · Zbl 1053.34055
[13] Ahmed, N. U., Vector measures for optimal control of impulsive systems in Banach spaces, Nonlinear Funct. Anal. Appl., 5, 2, 95-106 (2000) · Zbl 0982.49022
[14] Ahmed, N. U., Measure solutions impulsive evolution differential inclusion and optimal control, Nonlinear Anal., 47, 13-23 (2001) · Zbl 1042.49505
[15] Ahmed, N. U., Systems governed by impulsive differential inclusions on Hilbert spaces, Nonlinear Anal., 45, 693-706 (2001) · Zbl 0995.34053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.