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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 3, Pages 3–18
DOI: https://doi.org/10.26907/0021-3446-2019-3-3-18 (Mi ivm9443) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Solvability of inhomogeneous autonomous differential equation with aftereffect on the negative semi-axis

A. S. Balandin, T. L. Sabatulina

Perm National Research Polytechnic University, 29 Komsomol'skii Ave., Perm, 614990 Russia
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DOI: https://doi.org/10.26907/0021-3446-2019-3-3-18
Abstract: We obtain necessary and sufficient condition of solvability for a linear autonomous inhomogeneous functional differential equation with aftereffect and find the representation of all solutions in the special space of integrable functions with exponential weight. The obtained results are applied for study of two inhomogeneous differential equations with delay (the first equation is with concentrated delay, and the second one is with distributed delay). We give effective description of the space of solutions for these equations.
Keywords: functional differential equation, aftereffect, inhomogeneous equation, solvability on the axis, space of functions with exponential weight.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.5336.2017/8.9
Russian Foundation for Basic Research 18-01-00928_а
Received: 12.02.2018
Revised: 12.02.2018
Accepted: 20.06.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 3, Pages 1–14
DOI: https://doi.org/10.3103/S1066369X19030010
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: A. S. Balandin, T. L. Sabatulina, “Solvability of inhomogeneous autonomous differential equation with aftereffect on the negative semi-axis”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 3, 3–18; Russian Math. (Iz. VUZ), 63:3 (2019), 1–14
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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