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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2015, Number 2, Pages 36–41
(Mi basm390)
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Research articles
Solvability of a nonlinear integral equation arising in kinetic theory
A. Kh. Khachatryan, Kh. A. Khachatryan Institute of Mathematics of National Academy of Sciences of Armenia
Abstract:
In the paper the question of solvability of an Urysohn type nonlinear integral equation arising in kinetic theory of gases has been studied. We prove the existence of a positive and bounded solution and also suggest an approach for the construction of a solution. We also show that there is a qualitative difference between solutions in the linear and nonlinear cases. In the nonlinear case the solution is a positive and bounded function, while the corresponding linear equation has an alternating solution, which possesses linear growth at infinity.
Keywords and phrases:
nonlinear integral equation, monotony, iteration, pointwise convergence, bounded solution, linear growth.
Received: 21.10.2014
Citation:
A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear integral equation arising in kinetic theory”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 2, 36–41
Linking options:
https://www.mathnet.ru/eng/basm390 https://www.mathnet.ru/eng/basm/y2015/i2/p36
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