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Izvestiya: Mathematics, 2015, Volume 79, Issue 2, Pages 411–430
DOI: https://doi.org/10.1070/IM2015v079n02ABEH002748
(Mi im8245)
 

This article is cited in 14 scientific papers (total in 14 papers)

Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line

Kh. A. Khachatryan

Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan
References:
Abstract: We study certain classes of non-linear Hammerstein integral equations on the semi-axis and the whole line. These classes of equations arise in the theory of radiative transfer in nuclear reactors, in the kinetic theory of gases, and for travelling waves in non-linear Richer competition systems. By combining special iteration methods with the methods of construction of invariant cone segments for the appropriate non-linear operator, we are able to prove constructive existence theorems for positive solutions in various function spaces. We give illustrative examples of equations satisfying all the hypotheses of our theorems.
Keywords: Hammerstein equation, Carathéodory condition, monotonicity, induction, iterations, convergence.
Funding agency Grant number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia SCS 13YR-1A0003
This paper was written with the financial support of SCS MES RA under the scientific project no. SCS 13YR-1A0003.
Received: 18.04.2014
Bibliographic databases:
Document Type: Article
MSC: 45G05, 45M20
Language: English
Original paper language: Russian
Citation: Kh. A. Khachatryan, “Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line”, Izv. Math., 79:2 (2015), 411–430
Citation in format AMSBIB
\Bibitem{Kha15}
\by Kh.~A.~Khachatryan
\paper Positive solubility of some classes of non-linear integral equations
of Hammerstein type on the semi-axis and on the whole line
\jour Izv. Math.
\yr 2015
\vol 79
\issue 2
\pages 411--430
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Linking options:
  • https://www.mathnet.ru/eng/im8245
  • https://doi.org/10.1070/IM2015v079n02ABEH002748
  • https://www.mathnet.ru/eng/im/v79/i2/p205
  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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