Stability for a Class of Differential Equations with Nonconstant Delay

Abstract EN

Stability is investigated for the following differential equations with nonconstant delay x't=qtFxt-ptfxt-τt, where p:[0,+∞)→[0,+∞), q:[0,+∞)→R, τ:[0,+∞)→[0,r], and F and f:R→R with xfx>0  for  x≠0  and  x≤a (a is a positive constant) are continuous functions.

A criterion is given for the zero solution of this delay equation being uniformly stable and asymptotically stable.