Sentence examples for be the corresponding solution from inspiring English sources

Let y i be the corresponding solution.

Thus, let L = ( u, q, z ) be the corresponding solution of problem (2.9 - 2.17).

Let ((u t,x), b t,x))) be the corresponding solution of the initial value problem (1.1).

Theorem 2.2 Let u 0 ∈ H s ( R ) with s > 3 2, and u be the corresponding solution to (2.1) in Theorem  2.1.

Let (bar {u}(cdot)) be the optimal control for the cost function defined in (2) and let (bar {x}(cdot)) be the corresponding solution of equation (1).

Under the previous assumptions on (f u)), let c be an admissible speed for (7) and (y u)) be the corresponding solution.

Let g and g ˜ in W 1, ∞ and ω and ω ˜ be the corresponding solutions to (4.1).

Theorem 7 Let g and g ˜ be in W 1, ∞ , and let ω h and ω ˜ h be the corresponding solutions to (4.1).

end{aligned} Therefore S is a contraction, using Lemma 3.3, we see that (mathcal{N}) has at least one fixed point which is the corresponding solution of (2).

for all ( φ 0 h, φ 1 h ) ∈ V 0 h × V 0 h, where φ h is the corresponding solution of equation (2.2).

Therefore, by Theorem 2.7 the operator (mathbb{T}) has at least one fixed point, which is the corresponding solution to (1), and the set of the solutions is bounded in (mathcal{E}).