SOLVABILITY FOR A CLASS OF NON-LOCAL SEMI-LINEAR DIFFERENTIAL EQUATIONS WITH DELAYS

Abstract

In this article, we examine the solvency of mild solutions for a class of non-local semi-linear differential aquations involving finite delays. We prove the global solvability of mild solutions to this problem based on local estimates and fixed point arguments, in which the non-linearity is sub-linear without the smallness condition on initial data as well as on coefficients.