On alternating and bounded solutions of one class of integral equations on the entire axis with monotonic nonlinearity. (Russian. English summary) Zbl 1463.45021

Summary: The paper is devoted to the study of the existence and analysis of the qualitative properties of solutions for one class of integral equations with monotonic nonlinearity on the entire line. The indicated class of equations arises in the kinetic theory of gases. The constructive theorems of the existence of bounded solutions are proved, and certain qualitative properties of the constructed solutions are studied. At the end of the paper, specific applied examples of these equations are given.


45G05 Singular nonlinear integral equations
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[1] Kogan M. N., Rarefied Gas Dynamics, Springer Science, New York, 1969, xi+515 pp.
[2] Engibaryan N. B., Khachatryan A. Kh., “Some convolution-type integral equations in kinetic theory”, Comput. Math. Math. Phys., 38:3 (1998), 452-467 · Zbl 0949.45004
[3] Khachatryan Kh. A., “Solvability of a conservative integral equation on the half-line”, Izv. NAN Armenii. Matematika, 37:4 (2002), 73-80 (In Russian) · Zbl 1160.45300
[4] Khachatryan Kh. A., Sisakyan A. A., “On solvability of one class of nonlinear integral equations on whole line”, Vestn. of Russian-Armenian (Slavonic) Univ., 2017, no. 2, 25-40 (In Russian)
[5] Khachatryan A. Kh., Khachatryan Kh. A., “A nonlinear integral equation of Hammerstein type with a noncompact operator”, Sb. Math., 201:4 (2010), 595-606 · Zbl 1204.45006
[6] Khachatryan Kh. A., Grigoryan S. A., “On nontrivial solvability of a nonlinear Hammerstein-Volterra type integral equation”, Vladikavkaz. Mat. Zh., 14:2 (2012), 57-66 (In Russian) · Zbl 1326.45005
[7] Kolmogorov A. N., Fomin V. S., Elementy teorii funktsii i funktsional’nogo analiza [Elements of the theory of functions and functional analysis], Nauka, Moscow, 1976, 543 pp. (In Russian)
[8] Arabadzhyan L. G., Khachatryan A. S., “A class of integral equations of convolution type”, Sb. Math., 198:7 (2007), 949-966 · Zbl 1155.45002
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