Retarded Differential Equations with Piecewise Constant Delays

Profound and close links exist between functional and functional differential equations. Thus, the study of the first often enables one to predict properties of differential equations of neutral type. On the other hand, some methods for the latter in the special case when the deviation of the argument vanishes at individual points have been used to investigate functional equations [ 11. Functional equations are directly connected with difference equations of a discrete (for example, integer-valued) argument, the theory of which has been very intensively developed in the book [2] and in numerous subsequent papers. Bordering on difference equations are the impulse functional differential equations with impacts and switching, loaded equations (that is, those including values of the unknown solution for given constant values of the argument), equations