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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 2, Pages 205–224 (Mi izv8245)  

This article is cited in 4 scientific papers (total in 4 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

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.


DOI: https://doi.org/10.4213/im8245

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English version:
Izvestiya: Mathematics, 2015, 79:2, 411–430

Bibliographic databases:

MSC: 45G05, 45M20
Received: 18.04.2014

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. RAN. Ser. Mat., 79:2 (2015), 205–224; Izv. Math., 79:2 (2015), 411–430

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kh. A. Khachatryan, H. S. Petrosyan, “One parameter families of positive solutions of some classes of convolution type nonlinear integral equations”, J. Math. Sci., 231:2 (2018), 153–167  mathnet  crossref  crossref
    2. Kh. A. Khachatryan, A. K. Kroyan, “Suschestvovanie nechetnogo resheniya dlya odnoi granichnoi zadachi so stepennoi nelineinostyu”, Sib. zhurn. chist. i prikl. matem., 18:4 (2018), 88–96  mathnet  crossref
    3. Kh. A. Khachatryan, “O razreshimosti odnoi sistemy nelineinykh integralnykh uravnenii tipa Gammershteina na pryamoi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:2 (2019), 164–181  mathnet  crossref  elib
    4. Kh. A. Khachatryan, A. S. Petrosyan, “O postroenii summiruemogo resheniya odnogo klassa nelineinykh integralnykh uravnenii tipa Gammershteina - Nemytskogo na vsei pryamoi”, Tr. IMM UrO RAN, 26, no. 2, 2020, 278–287  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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