Sentence examples for satisfies exists from inspiring English sources

To provide the least restrictive condition to guarantee the well-posedness of the initial-value problem for equation (1.1) (see Definition 1 for the precise sense of well-posedness), we assume hereafter that B satisfies exists tin 0,infty text{ s.t.

If (T:Xrightarrow X) satisfies exists_{0leqlambda< 1}forall_{x,yin X}bigl{ dbigl(T x ,T y bigr)leq lambda d x,y bigr}, (1.1) then: (i) T has a unique fixed point w in X; and (ii) for each (w^{0}in X), (lim_{mrightarrowinfty}d(T^{[m]}(w^{0}), w)=0).

We prove that the optimal train fare satisfies: there exists a particular train station that has some seats and the train is full after this station.

Since T satisfies, there exists v y ∈ T y) such that.

We say that F satisfies ((ddag )) if the following conditions are satisfied: There exists (z_0ne 0) a critical point of (f_0), such that (f_t z_0) = t) for all t.

In (iii) the condition is satisfied when is continuous (since is compact) and the condition is satisfied when exists and is continuous.

Using the geometry of nonlinear dynamical systems we show that, providing certain constraints on the structure of time delays within the system are satisfied, there exists a neural controller that can render all the dynamics of the neuromusculoskeletal system (except for time delays) unobservable in the responses.

If conditions (H0), (H2″), (H8) and (H9) are satisfied, there exists a constant (mu^>0) such that problem (1.1) has at least one weak solution for (muin(mu^,infty)).

Assume in addition to (S 1) and (S 2), the following conditions are satisfied, there exists 0 < r < ξ 1 ρ T < ρ < ∞ such that.

A pseudocontraction semigroup of mappings from into itself is said to be Lipschitzian if the conditions (a)–(c), (e), and the following condition (f) are satisfied: there exists a bounded measurable function such that, for any, (1.4).

We have proven that when the conditions are satisfied, there exists a critical value τ 0 of the delay below which system (3) is stable and above which system (3) is unstable.