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CMFD, 2012, Volume 45, Pages 18–31 (Mi cmfd210)  

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

Approximate solution of nonlinear discrete equations of convolution type

S. N. Askhabov

Chechen State University, Grozny, Russia

Abstract: By the method of potential monotone operators we prove global theorems on existence, uniqueness, and ways to find a solution for different classes of nonlinear discrete equations of convolution type with kernels of special form both in weighted and in weightless real spaces $\ell_p$. Using the property of potentiality of the operators under consideration, in the case of space $\ell_2$ and in the case of a weighted space $\ell_p(\varrho)$ with a generic weight $\varrho$ we prove that a discrete equation of convolution type with an odd power nonlinearity has a unique solution and it (the main result) can be found by gradient method.

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English version:
Journal of Mathematical Sciences, 2014, 201:5, 566–580

Bibliographic databases:

UDC: 517.988.63

Citation: S. N. Askhabov, “Approximate solution of nonlinear discrete equations of convolution type”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, CMFD, 45, PFUR, M., 2012, 18–31; Journal of Mathematical Sciences, 201:5 (2014), 566–580

Citation in format AMSBIB
\Bibitem{Ask12}
\by S.~N.~Askhabov
\paper Approximate solution of nonlinear discrete equations of convolution type
\inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~1
\serial CMFD
\yr 2012
\vol 45
\pages 18--31
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd210}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3087047}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 201
\issue 5
\pages 566--580
\crossref{https://doi.org/10.1007/s10958-014-2012-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84905881458}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Askhabov S. N., Tovsultanov A. A., “Diskretnye uravneniya tipa svertki s monotonnoi nelineinostyu v prostranstvakh summiruemykh posledovatelnostei”, Vestn. Chechenskogo gos. universiteta, 2014, 21–29  mathscinet  elib
    2. S. N. Askhabov, “Nelineinye integralnye uravneniya s yadrami tipa potentsiala na otrezke”, Trudy Sedmoi Mezhdunarodnoi konferentsii po differentsialnym i funktsionalno-differentsialnym uravneniyam (Moskva, 22–29 avgusta, 2014). Chast 3, SMFN, 60, RUDN, M., 2016, 5–22  mathnet
  • Современная математика. Фундаментальные направления
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