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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On solvability in $ W_1^1(\mathbb{R}^+)$ of a nonlinear integro-differential equation with a noncompact Hammerstein-Nemytskiĭ operator


Author: Kh. A. Khachatryan
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 24 (2012), nomer 1.
Journal: St. Petersburg Math. J. 24 (2013), 167-183
MSC (2010): Primary 45J05
Published electronically: November 15, 2012
MathSciNet review: 3013298
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Abstract: A nonlinear first order integro-differential equation is studied; this equation has important applications to the kinetic theory of metals. Under some conditions on nonlinearity, the existence of a positive solution in the Sobolev class $ W_1^1(\mathbb{R}^+)$ is proved.


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Additional Information

Kh. A. Khachatryan
Affiliation: Institute of Mathematics, Armenian National Academy, Armenia
Email: Khach82@rambler.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01235-5
PII: S 1061-0022(2012)01235-5
Keywords: Sobolev space, Carathéodory condition, convergence of iterations, Hamerstein type equation
Received by editor(s): January 14, 2011
Published electronically: November 15, 2012
Article copyright: © Copyright 2012 American Mathematical Society