Sentence examples for exists suitable from inspiring English sources

Further, we may assume that u 1 ( x, 0 ) > 0 and u 2 ( x, 0 ) > 0 for x ∈ Ω, otherwise replace the initial function ( u 1 ( x, 0 ), u 2 ( x, 0 ) ) by ( u 1 ( x, t 1 ), u 2 ( x, t 1 ) ) for some t 1 > 0. Let ϕ ( x ) > 0 be the eigenfunction corresponding to the eigenvalue λ, then there exists suitable ε 0 > 0, such that ε 0 δ 1 ϕ ( x ) ≤ u 1 ( x, 0 ), ε 0 δ 2 ϕ ( x ) ≤ u 2 ( x, 0 ).

Because no human vaccine against S. suis exists, suitable preventive measures coupled with education and supervision of those who come in contact with live swine or unprocessed pork are important to decrease the transmission of this organism to humans.

Under the assumptions of Theorem  1.1, there exist suitable weak solutions (uin G), (thetain J) to problem (1.1 - 1.5).

Lemma 3.4 There exist suitable initial data such that v blows up while u remains bounded if and only if β > p. Proof Firstly, we prove the sufficiency.

Next, we will show that there exist suitable positive constants (D_{i}), (d_{i}), (a_{i}) ((i=1,2,ldots,suchsuch that inequalities (3.2) and (3.3) are satisfied.

Lemma 3.3 There exist suitable initial data such that u blows up while v remains bounded if and only if α > q + 1. Proof Firstly, we prove the sufficiency.

These instruments represent computable necessary and sufficient conditions for the existence of the properties (i), (ii), and whenever the property (ii) exists, a suitable state-feedback matrix is provided.

It is true if there exists a suitable covering, false otherwise.

∀ ε > 0, by the hypothesis, there exists a suitable δ > 0 such that (1.8) holds.

Since there exists a suitable constant such that, for all., the sequence turns out to be bounded in.

For all ε > 0, by the hypothesis, there exists a suitable δ > 0 such that (2.1) holds.