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Mat. Tr., 2012, Volume 15, Number 2, Pages 172–193 (Mi mt235)  

This article is cited in 1 scientific paper (total in 1 paper)

Nontrivial solvability of a class of nonlinear integro-differential equations of second order

Kh. A. Khachatryan

Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, Armenia

Abstract: The article is devoted to the study of nontrivial solvability and the asymptotic behavior of solutions for some classes of nonlinear integro-dofferential equations with a noncompact operator in a special case. Combining special factorization methods with the methods of the theory of linear integral equations of convolution type, we prove existence theorems for these classes of equations. With the help of a priori estimates, we calculate the limits of solutions obtained at infinity. The examples exhibited in the article are of mathematical interest in their own right. They are particular cases of the equations considered and have important applications in quantum mechanics.

Key words: factorization, Carathéodory condition, convergence of iterations, the limit of a solution.

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English version:
Siberian Advances in Mathematics, 2013, 23:4, 234–249

Bibliographic databases:

UDC: 517.968.74
Received: 19.10.2011

Citation: Kh. A. Khachatryan, “Nontrivial solvability of a class of nonlinear integro-differential equations of second order”, Mat. Tr., 15:2 (2012), 172–193; Siberian Adv. Math., 23:4 (2013), 234–249

Citation in format AMSBIB
\Bibitem{Kha12}
\by Kh.~A.~Khachatryan
\paper Nontrivial solvability of a~class of nonlinear integro-differential equations of second order
\jour Mat. Tr.
\yr 2012
\vol 15
\issue 2
\pages 172--193
\mathnet{http://mi.mathnet.ru/mt235}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3074462}
\elib{https://elibrary.ru/item.asp?id=18076210}
\transl
\jour Siberian Adv. Math.
\yr 2013
\vol 23
\issue 4
\pages 234--249
\crossref{https://doi.org/10.3103/S1055134413040020}


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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. Kh. A. Khachatryan, H. S. Petrosyan, “One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity”, Russian Math. (Iz. VUZ), 62:6 (2018), 43–55  mathnet  crossref  isi
  • Математические труды Siberian Advances in Mathematics
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