Thus, we have proved that (3.1) is true for every (tin[0,T)). Furthermore, by Lemma 3.2 we see that (3.2) is also valid on (tin[0,T)). Secondly, we prove that the solution of problem (1.1) blows up in a finite time. Assume by contradiction that the solution u is global.
Furthermore, for every (iin I), (T_{i}) are equal to the identity function, moreover the obtain in particular Darbo's (see [38]) as well as Sadovskii's (see [39]) fixed point theorems, which are used to study the existence of solutions of one equation.
Furthermore, for every withdrawal from an ATM £16 – amounting to £36bn a year – is injected directly into local stores, meaning more than a third of total high street spending is directly reliant on easy access to a cash machine.
Furthermore, for every, implies that,, where (3.5)., and.
Furthermore, for every n ∈ N and a.a. t ∈ [ 0, T ], we have ∥ x ¨ n ( t ) ∥ ≤ ϖ ( t ).
Furthermore, for every fixed (t>0), the continuity of u x, t) implies (H_{u}(t)) is an open set.
Furthermore, for every 100 L of beer produced 20 kg of BSG is generated during processing (Mussatto et al. 2006).
Furthermore, for every x ∈ X, the sequence ( ω p ( x ) ) p converges to e, where ω p = ω ∘ ω p − 1 (p time composition of ω), p ≥ 1.
Furthermore, for every continuous iterative root f of F of order (kgeq2) there exists a corresponding natural number (ell(f)), which maps I into (K(F)).
