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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.

34G25Evolution inclusions
34A37Differential equations with impulses
Full Text: DOI
[1] Ahmed, N. U.: Semigroup theory with applications to systems and control. Pitman res. Notes math. Ser. (1991)
[2] Pazy, A.: Semigroups of linear operators and applications to partial differential equations. (1983) · Zbl 0516.47023
[3] Li, Xunjing; Yong, Jiongmin: Optimal control theory for infinite dimensional systems. (1995)
[4] Lakshmikantham, V.; Bainov, D. D.; Simenov, P. S.: Theory of impulsive differential equations. (1999)
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[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, No. 1, 77-85 (1999) · Zbl 0932.34067
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[10] Rogovchenko, Y. V.: Impulsive evolution systems: Main results and new trends. Dyn. contin. Discrete impuls. Syst. 3, No. 1, 77-88 (1997) · Zbl 0879.34014
[11] Yu, Xiulan; Jiang, Yang: Impulsive perturbation of C0-semigroups and a class of semilinear impulsive evolution equation. J. guizhou university 20, No. 4, 350-357 (2003)
[12] Ahmed, N. U.: Impulsive perturbation of C0-semigroups and evolution inclusions. Nonlinear funct. Anal. appl. 9, No. 1, 127-147 (2004)
[13] Ahmed, N. U.: Vector measures for optimal control of impulsive systems in Banach spaces. Nonlinear funct. Anal. appl. 5, No. 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