SOME RESULTS IN THE EXISTENCE, UNIQUENESS AND STABILITY PERIODIC SOLUTION OF NEW VOLTERRA INTEGRAL EQUATIONS WITH SINGULAR KERNEL

Abstract

The aim of this work is to study the  existence, uniqueness and stability of periodic solutions of some classes for non-linear systems of new Volterra integral equations with singular kernel in two variables by using Riemann integrals.  Furthermore, we investigation the existence, uniqueness and stability of the fundamental tools employed in the analysis are based on applications by depending on the numerical-analytic method for studying the periodic solutions of ordinary differential equations which were introduced by Samoilenko.The study of such nonlinear Volterra integral equations with singular kernel leads us to improve and extend Samoilenko method. Thus the non-linear integral equations with singular kernel that we have introduced in the study become more general and detailed than those introduced by Butris .