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

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 $W_1^1(\mathbb R^+)$.