Abstract:
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.
Keywords:Volterra integral equation, periodic solutions of the boundary value problem, necessary and sufficient condition for the existence of periodic solutions of Volterra equation, the principle of condensed mappings, the generating equation, the condition of analyticity.