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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 10, Pages 26–37 (Mi ivm9287)  

This article is cited in 2 scientific papers (total in 2 papers)

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

A. S. Balandin, T. L. Sabatulina

Perm National Research Polytechnic University, 29 Komsomol’skii Ave., Perm, 614990 Russia
Full-text PDF (239 kB) Citations (2)
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Abstract: We consider a linear autonomous homogeneous functional differential equation on the real negative semi-axis. We prove that if solutions belong to the special space of functions with integral limitations, then the space of solutions is finite-dimensional and its basis is formed by the solutions of the form $(t^m\exp(pt))$ generated by the roots of the characteristic equation. In contrast to the spaces used earlier, the pointwise estimation of solutions is replaced by the integral one. We adduce examples of differential equations with aftereffect and give the effective description of the space of solutions for these equations.
Keywords: functional differential equation, aftereffect, solvability on the axis, space of functions with exponential weight.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 2014/152, проект № 1890
Received: 17.05.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, Volume 61, Issue 10, Pages 21–31
DOI: https://doi.org/10.3103/S1066369X17100048
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: A. S. Balandin, T. L. Sabatulina, “Solvability of autonomous differential equation with aftereffect on negative semi-axis”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 10, 26–37; Russian Math. (Iz. VUZ), 61:10 (2017), 21–31
Citation in format AMSBIB
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\by A.~S.~Balandin, T.~L.~Sabatulina
\paper Solvability of autonomous differential equation with aftereffect on negative semi-axis
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 10
\pages 26--37
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\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 10
\pages 21--31
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  • https://www.mathnet.ru/eng/ivm/y2017/i10/p26
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Full-text PDF :58
    References:51
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