Boundary-value problems with control for operator equations in Banach spaces
Abstract
UDC 517.935
In this paper, using the generalized inversion theory of operators, we establish a criterion for solvability and the general form of solutions of operator equations with control that are not everywhere solvable and of linear boundary-value problems for such operators in Banach spaces.
References
N. N. Krasovskiĭ, Теория управления движением (Russian) [[Theory of control of motion: Linear systems]] , Izdat. ``Nauka'', Moscow (1968).
R. Kalman, P. Falb, M. Arbib, Очерки по математической теории систем (Russian) [[Topics in mathematical system theory]], Izdat. ``Mir'', Moscow, (1971).
N. N. Danilov, Kurs matematicheskoj e`konomiki, SO RAN, Novosibirsk (2002).
V. M. Alekseev, V. M. Tikhomirov, S. V. Fomin, Оптимальное управление (Russian) Optimal`noe upravlenie, Fizmatlit, Moskva (2005).
D. E. Kirk, Optimal control theory: an introduction, Dover Publ., New York (2004).
O. A. Kapustyan, O. K. Mazur, Rozv'yaznist` zadachi optimal`nogo keruvannya z minimal`noyu energiyeyu dlya odniyeyi parabolichnoyi krajovoyi zadachi z nelokal`nimi krajovimi umovami, Zhurn. obchislyuv. ta prikl. matematiki, 120, № 3, 6 – 10 (2015).
V. I. Zubov, Postroenie programmny`kh dvizhenij v linejny`kh upravlyaemy`kh sistemakh, Differencz. uravneniya, 6, № 4, 632 – 633 (1970).
A. A. Bojchuk, V. F. Zhuravlev, A. M. Samojlenko, Normal`no razreshimy`e kraevy`e zadachi, Nauk. dumka, Kiev (2019).
O. A. Bojchuk, Ye. S. Vojtushenko, L. M. Shegda, Neterova impul`sna zadacha z keruvannyam, Nelinijni kolivannya, 19, № 3, 362 – 366 (2016).
I. A. Bondar, Umovi keruvannya dlya ne zavzhdi rozv'yaznikh integro-diferenczial`nikh rivnyan` z virodzhenim yadrom ta krajovikh zadach dlya nikh, Bukov. mat. zhurn., 4, № 1-2, 13 – 17 (2016).
I. Cz. Gokhberg, N. Ya. Krupnik, Vvedenie v teoriyu odnomerny`kh singulyarny`kh integral`ny`kh operatorov, Shtiincza, Kishinev (1973).
M. M. Popov, Dopovnyuval`ni prostori i deyaki zadachi suchasnoyi geometriyi prostoriv Banakha, Matematika s`ogodni'07, vip. 13, 78 – 116 (2007).
S. G. Kreĭn, Линейные уравнения в банаховом пространстве (Russian) [[Linear equations in a Banach space]], Izdat. ``Nauka'', Moscow, (1971).
V. F. Zhuravlev, Kriterij razreshimosti i predstavlenie reshenij linejny`kh $n- (d)$-normal`ny`kh operatorny`kh uravnenij v banakhovom prostranstve, Ukr. mat. zhurn., 62, № 2, 167 – 182 (2010).
V. F. Zhuravlev, N. P. Fomin, P. N. Zabrodskiy, Conditions of solvability and representation of the solutions of equations with operator matrices, Ukr. Math. J., 71, № 4, 537 – 552 (2019), https://doi.org/10.1007/s11253-019-01662-3 DOI: https://doi.org/10.1007/s11253-019-01662-3
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