Asymptotic stability of the complex dynamic equation uΔ - z.u+w.uσ=0

In this paper, we provide sharp conditions for the complex time scale exponential function tend to zero asymptotically. More precisely, we study the asymptotic stability of the unique complex solution u = e(z)circle minus(mu)w(.,s) of the initial value problem {u(Delta) - z center dot u + w center dot u(sigma) = 0 for t is an element of T u(s) = 1, where T is a time scale with sup T = infinity, s is an element of T. and z, w are complex constants. We also present an illustrative example to mention the sharpness of the main result. (c) 2014 Elsevier Inc. All rights reserved.