"Nothing out there exists".
What's more, even after the train passes across the embankment section, there exist larger permanent displacement residing in the embankment and more damages to the toe of the embankment slope on October 15.
The disease in model (1) is said to be weak permanent (permanent) if there exists a constant h > 0 such that, for any solution sequence ( x ( n ), y 1 ( n ), y 2 ( n ), …, y m ( n ), z ( n ) ) of model (1), one has lim sup n → ∞ y i ( n ) ≥ h ( lim inf n → ∞ y i ( n ) ≥ h ), i = 1, 2, …, m.
For model (2), disease (I(n)) is said to be permanent if there exists constants (M>m>0) such that for any solution ((S(n),E(n),I(n),R(n))) of model (2) with initial condition (3), (mleqliminf_{nrightarrowinfty}I(n) leqlimsup_{nrightarrowinfty}I(n leq M).
System (3) is said to be permanent if there exists positive constants m and M, with (0< m< M ) such that begin{aligned}& min Bigl{ liminf_{trightarrow+infty}P t),liminf_{trightarrow +infty}Z t) Bigr} geq m, & max Bigl{ limsup_{trightarrow+infty}P t),limsup_{trightarrow +infty}Z t) Bigr} leq M, end{aligned} for all solutions ((P t),Z(t))) of system (3) with positive initial values.
Species is called permanent if there exists a positive interval such that will ultimately enter and stay in this interval.
The system (1.3) is permanent if there exists such that, for any solution of the system (1.3) with, (3.12).
You are there, exist there.
The microorganism (x t) ) is said to be permanent in mean if there exists a positive constant λ such that (liminf_{trightarrow +infty } langle x t) rangle geq lambda ).
However, in some special and practical application scenarios [9], that is difficult to guarantee there always exists the permanent path between the source and destination.
