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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 43–49 (Mi into162)  
This article is cited in 2 scientific papers (total in 2 papers)

On lower estimates of solutions and their derivatives to a fourth-order linear integrodifferential Volterra equation

S. Iskandarova, G. T. Khalilovab

a Institute of Theoretical and Applied Mathematics of the National Academy of Sciences of the Kyrgyz Republic
b Kyrgyz-Russian Academy of Education
Full-text PDF (282 kB) Citations (2)
Abstract: We examine solutions of the problem on sufficient conditions that guarantee a lower estimate and tending to infinity of solutions and their derivatives up to the third order to a fourth-order linear integrodifferential Volterra equation. For this purpose, we develop a method based on the nonstandard reduction method (S. Iskandarov), the Volterra transformation method, the method of shearing functions (S. Iskandarov), the method of integral inequalities (Yu. A. Ved’ and Z. Pakhyrov), the method of a priori estimates (N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina, P. M. Simonov, 1991, 2001), the Lagrange method for integral representations of solutions to first-order linear inhomogeneous differential equations, and the method of lower estimate of solutions (Yu. A. Ved’ and L. N. Kitaeva).
Keywords: integrodifferential equation, a priori estimate, lower estimate, initial data, instability.
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 688–694
DOI: https://doi.org/10.1007/s10958-018-3770-8
Bibliographic databases:
Document Type: Article
UDC: 517.968.74
MSC: 53À40, 20Ì15
Language: Russian
Citation: S. Iskandarov, G. T. Khalilova, “On lower estimates of solutions and their derivatives to a fourth-order linear integrodifferential Volterra equation”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 43–49; J. Math. Sci. (N. Y.), 230:5 (2018), 688–694
Citation in format AMSBIB
\Bibitem{Isk17}
\by S.~Iskandarov, G. T. Khalilova
\paper On lower estimates of solutions and their derivatives to a fourth-order linear integrodifferential Volterra equation
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 43--49
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into162}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801382}
\zmath{https://zbmath.org/?q=an:1394.45009}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 688--694
\crossref{https://doi.org/10.1007/s10958-018-3770-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044445235}
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