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Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 6, Pages 48–62 (Mi ivm9367)  

One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity

Kh. A. Khachatryana, H. S. Petrosyanb

a Institute of Mathematics, National Academy of Sciences of Armenia, 24/5 Marshal Bagramyan Ave., Erevan, 0019 Armenia
b Armenian National Agrarian University, 74 Teryana str., Erevan, 0009, Armenia

Abstract: In the Sobolev space $W_\infty^2(\mathbb{R}^+)$ we investigate one initial boundary-value problem for integro-differential equation of the second order with power nonlinearity on a semi-axis. Assuming that summary-difference even kernel serves for the considered kernel as minorant in the sense of M.A. Krasnosel'skii, we prove the existence of nonnegative (nontrivial) solution in the Sobolev space $W_\infty^2(\mathbb{R}^+)$. We also calculate the limits of constructed solution at the infinity.

Keywords: nonnegative solution, iteration, limit of solution, Sobolev space, monotonicity.

Funding Agency Grant Number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia SCS 16YR-1A002


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:6, 43–55

Bibliographic databases:

UDC: 517.968
Received: 28.03.2017

Citation: Kh. A. Khachatryan, H. S. Petrosyan, “One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 6, 48–62; Russian Math. (Iz. VUZ), 62:6 (2018), 43–55

Citation in format AMSBIB
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\by Kh.~A.~Khachatryan, H.~S.~Petrosyan
\paper One initial boundary-value problem for integro-differential equation of the second order with power nonlinearity
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 6
\pages 48--62
\mathnet{http://mi.mathnet.ru/ivm9367}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2018
\vol 62
\issue 6
\pages 43--55
\crossref{https://doi.org/10.3103/S1066369X18060051}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047785919}


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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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