About new conditions of solvability of Chaplygin’s problem for integro-sum inequalities

Abstract

In the present work we sow some new conditions of the solvability of Chaplygin's problem for discontinuous functions which satisfy some integro-sum inequalities in one-dimensional and also in multidimensional case. We generalize some of the last results of the investigations of integro-sum inequalities in present of impulsive source by Agarwal, Akinyele, Borysenko, Iovane, Lakshmikantham, Samoilenko by using the results of Azbelev, Tsalyuk.