On positive solutions of one class of nonlinear integral equations of Hammerstein–Nemytskiĭ type on the whole axis
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Kh. A. Khachatryan
Translated by: E. Khukhro - Trans. Moscow Math. Soc. 2014, 1-12
- DOI: https://doi.org/10.1090/S0077-1554-2014-00226-0
- Published electronically: November 4, 2014
Abstract:
This paper is devoted to studying one class of nonlinear integral equations of Hammerstein–Nemytskiĭ type on the whole axis, which occurs in the theory of transfer in inhomogeneous medium. It is proved that these equations can be solved in various function spaces, and the asymptotic behaviour at infinity of the solutions that are constructed is studied.References
- C. Corduneanu, Integral equations and applications, Cambridge University Press, Cambridge, 1991. MR 1109491, DOI 10.1017/CBO9780511569395
- S. N. Askhabov and Kh. Sh. Mukhtarov, On a class of nonlinear integral equations of convolution type, Differentsial′nye Uravneniya 23 (1987), no. 3, 512–514, 550 (Russian). MR 886583
- P. P. Zabreĭko, A. I. Koshelev, M. A. Krasnosel’skiĭ, S. G. Mikhlin, L. S. Rakovshchik, and V. Ya. Stetsenko, Integral equations, Nauka, Moscow, 1968; English transl., Noordhoff Int. Publ., Leyden, Netherlands, 1975.
- Jürgen Appell and Petr P. Zabrejko, Nonlinear superposition operators, Cambridge Tracts in Mathematics, vol. 95, Cambridge University Press, Cambridge, 1990. MR 1066204, DOI 10.1017/CBO9780511897450
- N. B. Engibaryan, On a problem in nonlinear radiative transfer, Astrofizika 2 (1966), no. 1, 31–36; English transl., Astrophysics 2 (1966), no. 1, 12–14.
- V. V. Sobolev, A course on theoretical astrophysics, Nauka, Moscow, 1985. (Russian)
- J. D. Sargan, The distribution of wealth, Econometrica 25 (1957), 568–590. MR 95080, DOI 10.2307/1905384
- N. B. Engibaryan and A. Kh. Khachatryan, On the exact linearization of the sliding problem for a rarefied gas in the Bhatnagar-Gross-Krook model, Teoret. Mat. Fiz. 125 (2000), no. 2, 339–342 (Russian, with Russian summary); English transl., Theoret. and Math. Phys. 125 (2000), no. 2, 1589–1592. MR 1837692, DOI 10.1007/BF02551017
- N. B. Engibaryan and A. Kh. Khachatryan, Problems in the nonlinear theory of the dynamics of a rarefied gas, Mat. Model. 16 (2004), no. 1, 67–74 (Russian, with English and Russian summaries). MR 2060797
- A. Kh. Khachatryan and Kh. A. Khachatryan, Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases, Theoret. and Math. Phys. 172 (2012), no. 3, 1315–1320. Translation of Teoret. Mat. Fiz. 172 (2012), no. 3, 497–504. MR 3168751, DOI 10.1007/s11232-012-0116-4
- Norair B. Yengibarian, Renewal equation on the whole line, Stochastic Process. Appl. 85 (2000), no. 2, 237–247. MR 1731024, DOI 10.1016/S0304-4149(99)00076-9
- M. S. Sgibnev, On the uniqueness of the solution of a system of renewal-type integral equations on the line, Sibirsk. Mat. Zh. 51 (2010), no. 1, 204–211 (Russian, with Russian summary); English transl., Sib. Math. J. 51 (2010), no. 1, 168–173. MR 2654532, DOI 10.1007/s11202-010-0017-4
- Kenny S. Crump, On systems of renewal equations, J. Math. Anal. Appl. 30 (1970), 425–434. MR 257678, DOI 10.1016/0022-247X(70)90174-5
- M. S. Sgibnev, Systems of renewal-type integral operators on the line, Differ. Uravn. 40 (2004), no. 1, 128–137, 144 (Russian, with Russian summary); English transl., Differ. Equ. 40 (2004), no. 1, 137–147. MR 2167238, DOI 10.1023/B:DIEQ.0000028723.13032.f1
- N. B. Engibaryan, Conservative systems of integral convolution equations on the half-line and the whole line, Mat. Sb. 193 (2002), no. 6, 61–82 (Russian, with Russian summary); English transl., Sb. Math. 193 (2002), no. 5-6, 847–867. MR 1957953, DOI 10.1070/SM2002v193n06ABEH000660
- Aghavard Kh. Khachatryan and Khachatur A. Khachatryan, Hammerstein-Nemytskii type nonlinear integral equations on half-line in space $L_1(0,+\infty )\cap L_\infty (0,+\infty )$, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 52 (2013), no. 1, 89–100. MR 3202752
- Najeh Salhi and Mohamed Aziz Taoudi, Existence of integrable solutions of an integral equation of Hammerstein type on an unbounded interval, Mediterr. J. Math. 9 (2012), no. 4, 729–739. MR 2991162, DOI 10.1007/s00009-011-0147-3
- L. G. Arabadzhyan and A. S. Khachatryan, On a class of convolution-type integral equations, Mat. Sb. 198 (2007), no. 7, 45–62 (Russian, with Russian summary); English transl., Sb. Math. 198 (2007), no. 7-8, 949–966. MR 2354533, DOI 10.1070/SM2007v198n07ABEH003868
- A. N. Kolmogorov and S. V. Fomin, Èlementy teorii funktsiĭ i funktsional′nogo analiza, 5th ed., “Nauka”, Moscow, 1981 (Russian). With a supplement “Banach algebras” by V. M. Tikhomirov. MR 630899
Bibliographic Information
- Kh. A. Khachatryan
- Affiliation: Institute of Mathematics of National Academy of Sciences of Armenia
- Email: Khach82@rambler.ru, Khach82@mail.ru
- Published electronically: November 4, 2014
- © Copyright 2014 Kh. A. Khachatryan
- Journal: Trans. Moscow Math. Soc. 2014, 1-12
- MSC (2010): Primary 45GXX
- DOI: https://doi.org/10.1090/S0077-1554-2014-00226-0
- MathSciNet review: 3308598