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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 167, Pages 3–13 (Mi into483)  

Method of maximal monotonic operators in the theory of nonlinear integro-differential equations of convolution type

S. N. Askhabovab

a Chechen State Pedagogical Institute
b Chechen State University, Groznyi

Abstract: Using the method of maximal monotonic (in the Browder–Minty sense) operators, we prove global theorems on the existence and uniqueness of solutions for various classes of nonlinear integro-differential equations of convolution type in real spaces $L_p$, $1<p<\infty$, and present illustrative examples.

Keywords: positive operator, convolution operator, monotone operator, nonlinear integro-differential equation

Funding Agency Grant Number
Russian Foundation for Basic Research 18-41-200001


DOI: https://doi.org/10.36535/0233-6723-2019-167-3-13

Full text: PDF file (216 kB)
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UDC: 517.968
MSC: 45G10, 47J05

Citation: S. N. Askhabov, “Method of maximal monotonic operators in the theory of nonlinear integro-differential equations of convolution type”, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22Ц26, 2018. Part III, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 167, VINITI, Moscow, 2019, 3–13

Citation in format AMSBIB
\Bibitem{Ask19}
\by S.~N.~Askhabov
\paper Method of maximal monotonic operators in the theory of nonlinear integro-differential equations of convolution type
\inbook Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22Ц26, 2018. Part III
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 167
\pages 3--13
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into483}
\crossref{https://doi.org/10.36535/0233-6723-2019-167-3-13}
\elib{https://elibrary.ru/item.asp?id=42518506}


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