On the differences and similarities of the first order delay and ordinary differential equations

Abstract

The present paper is the first step in the systematic study of differences and similarities of the first order delay and ordinary differential equations. The continuous dependence of solutions to DDE on the time delay tending to zero is discussed and theorems guaranteeing continuous dependence are proved. The properties of nonnegativity and the blow-up phenomena for the solution to delay differential equation are studied. Conditions guaranteeing boundness of the solution to DDE are stated. Delay differential equations are considered in R n as well as in L p .