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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.

MSC:

34G25 Evolution inclusions
34A37 Ordinary differential equations with impulses
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[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
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