On periodic solutions of boundary value problem for quasilinear integral Volterra equations

The following problem is studied: under what conditions the periodic function is a solution of the Volterra integral equation with periodic coefficients. In this paper, we find sufficient conditions for the existence of periodic solutions of the boundary value problem for quasilinear integral Volterra equations that tend to the solution of a periodic boundary value problem for the generating equation. The principle of condensed mappings and the conditions for the analyticity of given functions are applied. The solution of the Volterra quasilinear integral equations is constructed in the space of continuous functions.