Mathematics & Physics 2015, 8(4), 416–425 УДК 517.9 On Solvability of one Class of Nonlinear Integral-differential Equation with Hammerstein Non-compact Operator Arising in a Theory of Income Distribution Aghavard Kh. <...> Khachatryan Khachatur A. Khachatryan∗ Tigran H. Sardaryan Institute of Mathematics of NAS RA Marshal Baghramyan, 24/5, Yerevan, 0009 Armenia Received 06.08.2015, received in revised form 03.09.2015, accepted 05.10.2015 In present paper we investigate a class of nonlinear integral- differential equation with Hammerstein noncompact operator which has direct application in a theory of income distribution. <...> We prove solvability of the class of equations in special weighted Sobolev space. <...> The results of numerical calculations are also presented. <...> A Khachatryan, Tigran H. Sardaryan On Solvability of one Class of Nonlinear . <...> Unknown function f (x) plays a role of distribution density, i.e. f (x) dx is a number of economic agents which have incomes in the interval (x,x+dx). <...> Function λ0 characterizes the growth of capital and savings, bankruptcy, disappearance of economic enterprises, taxes and etc. <...> Function λ1 (x,u) describes nonlinear dependence of distribution function. <...> For the first time above mentioned class of nonlinear equations was studied by A. Kh. <...> The peculiarity of corresponding nonlinear integro-differential equations and complexity of their study are the following: ∫ +∞ −∞ 1. <...> A Khachatryan, Tigran H. Sardaryan On Solvability of one Class of Nonlinear . <...> Algorithm of numerical solution of this equation is described and some results of numerical calculations are given. 1. <...> A Khachatryan, Tigran H. Sardaryan On Solvability of one Class of Nonlinear . <...> It is easy to check by induction with respect to n that ψn (x) ↑ by n, x ∈ R+. <...> Moreover, due to Carathedory condition (see condition с)) and B. Levi’s theorem the limit function ψ satisfies equation (25). <...> Firstly, we √ρ ∂u = ε (x))=2 γ ρ ε (x) is continuous on R+ЧR+ with respect to all arguments, and hence satisfies Caratheodory condition on R+ЧR+ with respect to second argument. <...> Algorithm of numerical solution and results of numerical calculations A brief description of algorithm of numerical calculations are given in this section. <...> Fourth Step. "Mean income” is determined from the following relation: M= where <...>