Solvability of a Class of Integro-Differential Equations of First Order with Variable Coefficients

In the present paper, we consider a class of linear integro-differential equations of first order with a stochastic kernel and with variable coefficients on the semiaxis. These equations have important applications in physical kinetics. By combining special factorization methods with methods involving integral Fredholm equations of the second kind, we can construct solutions of such equations in the Sobolev space $W^1_1(\mathbb R^+)$. In certain singular cases, we can also describe the structure of the obtained solutions.