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.
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.
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.
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.
Not all database entries for which SDF files exist are suitable for assignment of InChI identifiers.
In particular, they have shown that if β ≥ 1 − η, then positive solutions exist under suitable conditions on f.
Little consensus exist in suitable tooth preparation design and alloy pre-treatment methods for improving the retention of resin bonded fixed partial dentures (RBFPDs).
Nonetheless, it is not entirely implausible to think such worlds exist given suitable duplication and reorganization of microphysical objects.[23] Whether recombination completely captures our modal intuitions regarding plenitude is still a matter of some dispute.[24] However, even if it doesn't, it is less than clear whether this counts against the success of Lewis's reductionist project.
For La x Gd1 x PO4: Eu3+, the luminescent lifetime reaches the longest (3.43 ms) at the x = 0.5, which is much longer than the other two compositions (x = 0.1 or 0.9), suggesting there exist a suitable molar ratio of La3+ to Gd3+ (1:1) for the luminescence of Eu3+.
