3(dx,t____~ =A( t ) x ( t )+ f ( t , x ( t ) ) , x ( t r l ( t ) ) , . . . , x ( t f k (t)), (1) dt such that the associated homogeneous linear system satisfies exponential dichotomy and deviations of the argument axe not restricted by any sign assumption. The exponential stability of the solution when the system is with delay argument is considered. (~) 2004 Elsevier Ltd. All rights reserved. ...

Consider the Liénard equation with a deviating argument x (t)+ f (x(t))x (t)+ g1(x(t))+ g2(x(t − τ(t))) = e(t), where f, g1 and g2 are continuous functions on R = (−∞,+∞), τ (t) ≥ 0 is a bounded continuous function on R, and e(t) is a bounded continuous function on R = [0,+∞). We obtain some new sufficient conditions for all solutions and their derivatives to be bounded, which substantially ext...

We consider mixed problems for infinite systems of first order partial functional differential equations. Infinite number of deviating functions is permitted, and the delay of an argument may depend also on spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existenc...