Generalization of practical stability for delay differential equations with respect to initial time difference.

A new definition of a stability nonlinear delay differential equations is introduced and studied. This type of stability generalizes the known in the literature practical stability and it is a generalization in two directions - the behavior of two nonzero solutions are compared; - the solutions are with different initial data - different initial time intervals as well as different initial functions. The introduced concept of stability is an extension of the studied up today types of stability and it gives a new tool for more adequate investigating of real world problems in science, engineering, technologies. Several sufficient conditions are obtained. Lyapunov functions as well as comparison results for scalar ordinary differential equations have been employed. [ABSTRACT FROM AUTHOR]