then (23) with [lambda] < 0 and the increasing order function v() is asymptotically
[[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
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
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 , 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
By Lyapunov global asymptotic stability theory, we can conclude system (12) is globally asymptotically
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
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