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Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces. (English) Zbl 1185.93016
Summary: Control problems appear in many branches of physics and technical science. In this paper we investigate the controllability of semilinear differential equations and inclusions via the semigroup theory in Banach spaces. All results are obtained by using fixed point theorems both for single and multivalued mappings.

MSC:
93B05Controllability
34G20Nonlinear ODE in abstract spaces
34K30Functional-differential equations in abstract spaces
47D06One-parameter semigroups and linear evolution equations
47N70Applications of operator theory in systems theory, circuits, and control theory
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References:
[1] Balachandran, K.; Antoni, M.: Controllability of second order semilinear ordinary differential systems in Banach spaces. J. appl. Math. stochastic anal. 12, 265-277 (1999) · Zbl 0989.93013
[2] Balachandran, K.; Anthoni, M.: Controllability of second-order semilinear neutral functional differential systems in Banach spaces. Comput. math. Appl. 41, 1223-1235 (2001) · Zbl 0990.93007
[3] Balachandran, K.; Anthoni, M.: Controllability of second order semilinear delay integrodifferential systems in Banach spaces, dedicated to emeritus Professor corneliu constantinescu on the occasion of his 70th birthday. Libertas math. 20, 79-88 (2000)
[4] Arendt, W.: Vector valued Laplace transforms and Cauchy problems. Israel J. Math. 59 (1987) · Zbl 0637.44001
[5] Balachandran, K.; Sakthivel, R.: A note on controllability of semilinear integrodifferential systems in Banach spaces. J. appl. Math. stochastic anal. 13, 161-170 (2000) · Zbl 0964.93010
[6] Balachandran, K.; Sakthivel, R.: Controllability of integrodifferential systems in Banach spaces. Appl. math. Comput. 118, 63-71 (2001) · Zbl 1034.93005
[7] Balachandran, K.; Sakthivel, R.: Controllability of functional semilinear integrodifferential systems in Banach spaces. J. math. Anal. appl. 255, 447-457 (2001) · Zbl 0982.93018
[8] Balachandran, K.; Sakthivel, R.: Controllability of Sobolev-type semilinear integrodifferential systems in Banach spaces. Appl. math. Lett. 12, 63-71 (1999) · Zbl 0951.93008
[9] Balachandran, K.; Sakthivel, R.: Controllability of semilinear functional integrodifferential systems in Banach spaces. Kybernetika (Prague) 36, 465-476 (2000) · Zbl 1249.93017
[10] Balachandran, K.; Sakthivel, R.; Dauer, J. P.: Controllability of neutral functional integrodifferential systems in Banach spaces. Comput. math. Appl. 39, 117-126 (2000) · Zbl 0982.93019
[11] Balachandran, K.; Manimegalai, P.: Controllability of nonlinear abstract neutral evolution integrodifferential systems. Nonlinear funct. Anal. appl. 7, 85-100 (2002) · Zbl 0997.93012
[12] Benchohra, M.; Górniewicz, L.; Ntouyas, S. K.: Controllability of some nonlinear systems in Banach spaces. (2003) · Zbl 1059.49001
[13] Bressan, A.; Colombo, G.: Extensions and selections of maps with decomposable values. Studia math. 90, 69-86 (1988) · Zbl 0677.54013
[14] Da Prato, G.; Sinestrari, E.: Differential operators with non-dense domains. Ann. scuola. Norm. sup. Pisa sci. 14, 285-344 (1987) · Zbl 0652.34069
[15] Fattorini, H. O.: Second order linear differential equations in Banach spaces. 108 (1985) · Zbl 0564.34063
[16] Gatsori, E.; Górniewicz, L.; Ntouyas, S. K.: Controllability results for nondensely defined evolution impulsive differential inclusions with nonlocal conditions. Panamer. math. J. 15, 1-27 (2005) · Zbl 1075.93003
[17] Goldstein, J. A.: Semigroups of linear operators and applications. (1985) · Zbl 0592.47034
[18] Granas, A.; Dugundji, J.: Fixed point theory. (2003) · Zbl 1025.47002
[19] Hale, J. K.; Kato, J.: Phase space for retarded equations with infinite delay. Funkcial. ekvac. 21, 11-41 (1978) · Zbl 0383.34055
[20] Heikkila, S.; Lakshmikantham, V.: Monotone iterative techniques for discontinuous nonlinear differential equations. (1994)
[21] Kang, J. -R.; Kwun, Y. -C.; Park, J. -Y.: Controllability of the second-order differential inclusion in Banach spaces. J. math. Anal. appl. 285, 537-550 (2003) · Zbl 1049.93008
[22] Kellerman, H.; Hieber, M.: Integrated semigroups. J. funct. Anal. 84, 160-180 (1989) · Zbl 0689.47014
[23] Liu, B.: Controllability of nonlinear neutral evolution integrodifferential systems with infinite delay. J. optim. Theory appl. 122, 87-109 (2004) · Zbl 1130.93313
[24] Liu, B.: Controllability of neutral functional differential and integrodifferential inclusions with infinite delay. J. optim. Theory appl. 123, 573-593 (2004) · Zbl 1175.93036
[25] Liu, B.: Controllability of impulsive neutral functional differential inclusions with infinite delay. Nonlinear anal. 60, 1533-1552 (2005) · Zbl 1079.93008
[26] Park, Y. -J.; Kwun, Y. -C.; Lee, H. L.: Controllability of second-order neutral functional differential inclusions in Banach spaces. J. math. Anal. appl. 285, 37-49 (2003) · Zbl 1025.93006
[27] Pazy, A.: Semigroups of linear operators and applications to partial differential equations. (1983) · Zbl 0516.47023
[28] Sakthivel, R.; Choi, Q. H.; Anthoni, S.: Controllability of nonlinear neutral evolution integrodifferential systems. J. math. Anal. appl. 275, 402-417 (2002) · Zbl 1010.93055
[29] Sakthivel, R.; Choi, Q. H.; Anthoni, S.: Controllability result for nonlinear evolution integrodifferential systems. Appl. math. Lett. 17, 1015-1023 (2004) · Zbl 1072.93005
[30] Sakthivel, R.; Choi, Q. H.: A study on controllability of semilinear integrodifferential systems in Banach spaces. Comput. math. Appl. 47, 519-527 (2004) · Zbl 1155.93331
[31] Travis, C.; Webb, G.: Existence and stability for partial functional differential equations. Trans. amer. Math. soc. 200, 395-418 (1974) · Zbl 0299.35085
[32] Travis, C.; Webb, G.: Cosine families and abstract nonlinear second order differential equations. Acta math. Hungarica 32, 75-96 (1978) · Zbl 0388.34039
[33] Travis, C.; Webb, G.: An abstract second order semilinear Volterra integrodifferential equation. SIAM J. Math. anal. 10, 412-424 (1979) · Zbl 0406.45014
[34] Wang, L.; Wang, Z.: Controllability of abstract neutral functional differential systems with infinite delay. Dyn. contin. Discrete impuls. Syst. ser. B appl. Algorithms 9, 59-70 (2002) · Zbl 1001.93005