Consider the rst order delay diierential equation x 0 (t) + p(t)x(t ?) = 0; > 0; t t 0 ; () and its discrete analogue Oscillation criteria are established for () in the case where 0 < liminf t!1 R t t? p (s) 1 e and limsup t!1 R t t? p(s)ds < 1, and for () 0 when liminf n!1 n?1 P i=n?k p i k k+1 k+1 and limsup n!1 n P i=n?k p i < 1. reziume. naSromSi ganxil u l ia pir vel i rigis dagvianebu l a...

Abstract The functional equations, functional integral equations and functional differential equations have many applications in nonlinear analysis. Also, the fractional order integral equations and fractional order differential equations have many applications in mathematical physics. Here we study the existence of solutions of a functional integral equations of arbitrary (fractional) order in...

We study evolution semigroups associated with nonautonomous functional differential equations. In fact, we convert a given functional differential equation to an abstract autonomous evolution equation and then derive a representation theorem for the solutions of the underlying functional differential equation. The representation theorem is then used to study the boundedness and almost periodici...

Differential equations with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and technology. Recently a well developed stability theory of functional differential systems has come into existence [15-21]. Qualitative properties of impulsive differential equations have been intensively researched for years. In [3-11], by using lyapunov...