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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     title = {On the solvability of one class of boundary-value problems for non-linear integro-differential equation in kinetic theory of plazma},
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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/