CONVERGENCE IN AN IMPULSIVE ADVANCED DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT (COMMUNICATED BY IOANNIS P. STAVROULAKIS)

In this work, we show the existence and uniqueness of the solution x (t) of the initial value problem { x' (t) = alpha (t) (x (t) - x ([t + 1])) + f (t), t not equal n is an element of Z(+) = {1,2,...}, t >= 0, Delta x (n) = d (n), n is an element of Z(+), x (0) = x(0). Moreover, we prove that the limit of x (t) is equal to a real constant as t -> infinity. Also, we formulate this limit value in terms of the initial condition, impulses, and the solution of an integral equation.