Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 192, Pages 26–37
DOI: https://doi.org/10.36535/0233-6723-2021-192-26-37 (Mi into778) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Gradient method for solving nonlinear discrete and integral equations with difference kernels

S. N. Askhabovab

a Chechen State University, Groznyi
b Chechen State Pedagogical Institute
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DOI: https://doi.org/10.36535/0233-6723-2021-192-26-37
Abstract: The method of potential monotonic operators (called also the Browder–Minty method) is used to prove global theorems on the existence and uniqueness of solutions for discrete and integral equations with difference kernels and odd-power nonlinearities. Using the gradient method (or the steepest descent method), we construct successive approximations that converge to the solutions mentioned with respect to the norm.
Keywords: monotonic operator, potential operator, nonlinear discrete equation, nonlinear integral equation.
Funding agency Grant number
Russian Foundation for Basic Research 18-41-200001
This work was supported by the Russian Foundation for Basic Research (project No. 18-41-200001).
Document Type: Article
UDC: 517.968.4
MSC: 45G10, 47J05
Language: Russian
Citation: S. N. Askhabov, “Gradient method for solving nonlinear discrete and integral equations with difference kernels”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 192, VINITI, Moscow, 2021, 26–37
Citation in format AMSBIB
\Bibitem{Ask21}
\by S.~N.~Askhabov
\paper Gradient method for solving nonlinear discrete and integral equations with difference kernels
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 3
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 192
\pages 26--37
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into778}
\crossref{https://doi.org/10.36535/0233-6723-2021-192-26-37}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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