Geodesic
On the solvability of one class of boundary-value problems for non-linear integro-differential equation in kinetic theory of plazma
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 451-461.

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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, monotonicity, iteration, Caratheodory's condition, Sobolev space.
Mots-clés : kernel 
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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. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 451-461. http://geodesic.mathdoc.fr/item/JSFU_2013_6_4_a5/

[1] E. M. Lifshits, L. M. Pitaevskii, Theoretical Physics, v. 10, Physical kinetics, Nauka, Moscow, 1979 (in Russian)

[2] Kh. A. Khachatryan, “On Solvability one Hammerstein–Nemitski type nonlinear integro-differential equation with noncompact operator in $W_1^1(\mathbb R^+)$”, St. Petersburg Matematicheskij Zhurnal (Algebra i Analiz), 24:1 (2012), 223–247 (in Russian) | MR

[3] Kh. A. Khachatryan, “Integro-differential equations of physical kinetics”, Jounal of Contemporary Mathematical Analysis, 39:3 (2004), 49–57 | MR

[4] L. G. Arabadzhyan, N. B. Engibaryan, “Convolution Equations and Nonlinear Functional Equations”, Itogi Nauki Tekh., Ser. Mat. Anal., 22, 1984, 175–244 (in Russian) | MR | Zbl

[5] L. A. Lusternik, V. I. Sobolev, Short course of functional analysis, Vysshaya shkola, Moscow, 1982 (in Russian)

[6] A. N. Kolmogorov, S. V. Fomin, Elements of theory of functions and functional analysis, Nauka, Moscow, 1981 (in Russian) | MR

[7] B. M. Budak, S. V. Fomin, Multiple integrals and series, Nauka, Moscow, 1965 (in Russian) | MR | Zbl