Sentence examples for solutions let us from inspiring English sources

To prove the existence and uniqueness of viscosity solutions, let us see the following main hypotheses first.

end{aligned} (3.1) Before computing the solutions, let us state explicitly the limitations that RL, considered as an order 2 polynomial on (D^{2}), that is, (RL x)=a x^{2}+b x +c), has no negative roots implies.

Since we are looking for nodal solutions, let us consider the so-called nodal Nehari set mathcal{N}_{epsilon}^{pm}= bigl{ v intilde{H}; v^{pm}neq0 mbox{ and } I_{epsilon}' v v^{pm}= 0bigr}.

In order to describe further these solutions, let us consider their energy at the time t + that we denote by k 1, k 2, k 3, with ℓ ∗ < k 3 < k 2 < k 1 < ℓ 0. Let us define the points H i as { H i } = O ( P + ) ∩ Γ k i for i = 1, 2, 3.

In order to implement climate solutions, let us stop the TiSA, along with the TPP, and the TTIP.

As we craft new solutions, let us not forget to preserve the old ones -- and to honor the memory of those who worked so hard to give us so much.

To show that model (2) has a positive global solution, let us firstly prove that the model has a positive local solution by making a change of variables.

To obtain a positive solution, let us construct a cone K by K = { x ∈ Q : x ( t ) ≥ e ( t ) x ( s ), t, s ∈ I } (2.2).

In our article, we are going to study the large time asymptotic behavior for the solution of (1.1) and (1.2) by comparing it to the Barenblatt-type solution, let us give some details.

For a feasible solution, let us choose (gamma _{i} = frac {1}{binom {k-1}{l-1}}) when L i ⊆K∗, and γ i =0 otherwise, which we can easily check whether it satisfies the first and second constraints of (15).

Before proving that the successive updates of the proposed method converge to the optimal solution, let us establish the relationship between primal and dual variables in the subproblems with the following proposition.