then (23) with [lambda] < 0 and the increasing order function v() is

asymptotically stable.

[[rho].sub.a](k, L,[eta],[p.sub.1],[p.sub.2])) is positive and

asymptotically increasing in k for 0 < k < [cL.sup.-1/2] and L small enough if

It is said that f [member of] [L.sup.p.sub.S]([0, [infinity]) : X) is

asymptotically Stepanov p-almost periodic,

asymptotically S^-almost periodic for short, iff [??] : [0, [infinity]) [right arrow] [L.sup.p]([0,1] : X) is

asymptotically almost periodic.

Therefore, for [R.sup.*.sub.1] < [R.sup.thr.sub.1], system (1) presented the locally

asymptotically stable low-criminality equilibrium [P.sub.l].

Obviously if [R.sub.0] < 1 disease-free equilibrium [E.sub.02] is locally

asymptotically stable; otherwise [E.sub.02] is unstable.

Therefore, the zero solution of system (6) is

asymptotically stable.

Xie, "Global attractivity of

asymptotically almost periodic Nicholson's blowflies models with a nonlinear densitydependent mortality term," International Journal of Biomathematics, vol.

By the method in [48], the point [E.sup.*]([x.sup.*], [y.sup.*]) is globally

asymptotically stable (see Figure 1.)

By the LaSalle's invariance principle, [E.sub.1] is globally

asymptotically stable.

By Lyapunov global asymptotic stability theory, we can conclude system (12) is globally

asymptotically stable.

We remark here that, in the discussion above, the cavity radius is introduced as a state parameter to test the thermodynamic properties near the critical point of the RN black hole in the

asymptotically flat space-time.

For a given [gamma] > 0, the time-delay system (14) is

asymptotically stable with [[parallel][T.sub.wz](s)[parallel].sub.[infinity]] < [gamma], if there exist positive definite matrices P, [Q.sub.1], [Q.sub.2], [R.sub.1], [R.sub.2], [S.sub.1], and [S.sub.2] and matrices [M.sub.1], [M.sub.2], [N.sub.1], [N.sub.2], [U.sub.1], [U.sub.2], [V.sub.1] and [V.sub.2] with appropriate dimensions such that