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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 815–828
DOI: https://doi.org/10.17377/semi.2016.13.065 (Mi semr715) 		 
Differentical equations, dynamical systems and optimal control

The correctness of a family of integral and delay differential equations, used in models of living systems

N. V. Pertseva, B. Yu. Pichugina, A. N. Pichuginab

a Sobolev Institute of Mathematics, Pevtsova st., 13, 644043, Omsk, Russia
b Omsk State University, pr. Mira, 55A, 644077, Omsk, Russia
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DOI: https://doi.org/10.17377/semi.2016.13.065
Abstract: We consider a family of integral equations arising in mathematical models of some living systems. Depending on the choice of the survival of elements of living systems integral equation is reduced to the equivalent of the Cauchy problem for non-autonomous differential equations with a point or distributed delays. Problems of existence, uniqueness, nonnegativity and extendibility of solutions are investigated.
Keywords: integral equation, delay differential equation, properties of solutions, mathematical model, living systems.
Received March 19, 2016, published October 6, 2016
Bibliographic databases:
Document Type: Article
UDC: 517.968.4+517.929
MSC: 45G10+34K05
Language: Russian
Citation: N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “The correctness of a family of integral and delay differential equations, used in models of living systems”, Sib. Èlektron. Mat. Izv., 13 (2016), 815–828
Citation in format AMSBIB
\Bibitem{PerPicPic16}
\by N.~V.~Pertsev, B.~Yu.~Pichugin, A.~N.~Pichugina
\paper The correctness of a family of integral and delay differential equations, used in models of living systems
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 815--828
\mathnet{http://mi.mathnet.ru/semr715}
\crossref{https://doi.org/10.17377/semi.2016.13.065}
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