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Avtomat. i Telemekh., 2011, Issue 6, Pages 127–132 (Mi at2231)  

This article is cited in 8 scientific papers (total in 8 papers)

Nonlinear Systems

Generalized solutions in the problem of dynamical systems modeling by Volterra polynomials

D. N. Sidorovab, N. A. Sidorova

a Irkutsk State University, Irkutsk, Russia
b Melentiev Energy Systems Institute, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

Abstract: We consider generalized solutions of polynomial integral Volterra equations of the first kind that arise in a control problem for nonlinear dynamical processes of the “input–output” type. We prove the existence theorem and propose a method for constructing generalized solutions. We establish that the number of solutions equals the number of roots of a certain polynomial.

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English version:
Automation and Remote Control, 2011, 72:6, 1258–1263

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Presented by the member of Editorial Board: . . 

Received: 16.12.2010

Citation: D. N. Sidorov, N. A. Sidorov, “Generalized solutions in the problem of dynamical systems modeling by Volterra polynomials”, Avtomat. i Telemekh., 2011, no. 6, 127–132; Autom. Remote Control, 72:6 (2011), 1258–1263

Citation in format AMSBIB
\by D.~N.~Sidorov, N.~A.~Sidorov
\paper Generalized solutions in the problem of dynamical systems modeling by Volterra polynomials
\jour Avtomat. i Telemekh.
\yr 2011
\issue 6
\pages 127--132
\jour Autom. Remote Control
\yr 2011
\vol 72
\issue 6
\pages 1258--1263

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sidorov D.N., Sidorov D.N., “Ob odnom klasse nelineinykh uravnenii i roda s odnorodnymi integralnymi operatorami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya: Matematika, 4:1 (2011), 109–117  mathnet  mathscinet  zmath  elib
    2. A. S. Apartsin, “Polinomialnye integralnye uravneniya Volterra I roda i funktsiya Lamberta”, Tr. IMM UrO RAN, 18, no. 1, 2012, 69–81  mathnet  elib
    3. S. V. Solodusha, “Modelirovanie sistem avtomaticheskogo upravleniya na osnove polinomov Volterra”, Model. i analiz inform. sistem, 19:1 (2012), 60–68  mathnet
    4. D. N. Sidorov, “O razreshimosti uravnenii Volterra I roda s kusochno-nepreryvnymi yadrami v klasse obobschennykh funktsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:1 (2012), 80–95  mathnet
    5. D. N. Sidorov, “Solvability of systems of integral Volterra equations of the first kind with piecewise continuous kernels”, Russian Math. (Iz. VUZ), 57:1 (2013), 54–63  mathnet  crossref
    6. N. A. Sidorov, D. N. Sidorov, “On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels”, Math. Notes, 96:5 (2014), 811–826  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Sidorov N., Sidorov D., Dreglea A., “Solvability and Bifurcation of Solutions of Nonlinear Equations With Fredholm Operator”, Symmetry-Basel, 12:6 (2020), 912  crossref  isi  scopus
    8. Kazakov A., Spevak L., Nefedova O., Lempert A., “On the Analytical and Numerical Study of a Two-Dimensional Nonlinear Heat Equation With a Source Term”, Symmetry-Basel, 12:6 (2020), 921  crossref  isi
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