Sentence examples for be a nonnegative solution from inspiring English sources

Let be a nonnegative solution of (1.11).

Let u be a nonnegative solution of (1.1) and (1.2).

Let (u in{C [0, T); G^{s}(mathbb{R}_))cap C^{1}([0, T); G^{s-1}(mathbb{R}_) be a nonnegative solution of (1.1) for all (T >0), Then the (2.1) has a unique solution (q in C^{1}([0, T timesmathbb{R}_, mathbb{R}_)). Moreover, the map (q t,cdot)) is an increasing diffeomorphism of (mathbb{R}_).

Moreover, there exist constants ϵ > 0 small enough and M > 0 large enough such that any nonnegative solution u of (1.1) is positive on I ˆ whenever dist ( λ, [ μ 1 f ∞, λ 1 f ∞ ] ) < ϵ and ∥ u ∥ ≥ M. Proof Let ( μ j, y j ) be a nonnegative solution of (1.1) with λ = μ j ∈ such that ∥ y j ∥ → ∞, and μ j → μ ˆ as  j → ∞. (2.7).

Moreover, is a nonnegative solution to (2.19).

Thus is a nonnegative solution of (1.1)−(1.4).

Assume that holds, and is a nonnegative solution of (1.11).

By Lemma 2.2, is a nonnegative solution of (1.5).

Hence ( λ, U ) is a nonnegative solution of (3.25).

Assume that and is a nonnegative solution of (1.11).

Thus, u is a nonnegative solution of (1 -(4).