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 J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 4, Pages 451–461 (Mi jsfu337)

On the solvability of one class of boundary-value problems for non-linear integro-differential equation in kinetic theory of plazma

Khachatur A. Khachatryana, Tsolak E. Terdjyanb, Haykanush S. Petrosyanb

a Institute of Mathematics of NAS, Marshal Baghramyan, 24/5, Yerevan, 0009 Armenia
b Armenian National Agrarian University, Teryan, 74, Yerevan, 0009 Armenia

Abstract: The work is devoted to the investigation of one class of non-linear integro-differential equations with the Hammerstein non-compact operator on the half-line. The mentioned class of equations has direct application in the kinetic theory of plazma. Combining the special factorization methods with the theory of construction of invariant cone intervals for non-linear operators permits to prove the existence of a solution of the initial equation in the Sobolev space $W_1^1(\mathbb R^+)$.

Keywords: factorization, kernel, monotonicity, iteration, Caratheodory's condition, Sobolev space.

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UDC: 519.21
Accepted: 06.09.2013
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Citation: Khachatur A. Khachatryan, Tsolak E. Terdjyan, Haykanush S. Petrosyan, “On the solvability of one class of boundary-value problems for non-linear integro-differential equation in kinetic theory of plazma”, J. Sib. Fed. Univ. Math. Phys., 6:4 (2013), 451–461

Citation in format AMSBIB
\Bibitem{KhaTerPet13} \by Khachatur~A.~Khachatryan, Tsolak~E.~Terdjyan, Haykanush~S.~Petrosyan \paper On the solvability of one class of boundary-value problems for non-linear integro-differential equation in kinetic theory of plazma \jour J. Sib. Fed. Univ. Math. Phys. \yr 2013 \vol 6 \issue 4 \pages 451--461 \mathnet{http://mi.mathnet.ru/jsfu337}