Sentence examples for the maximal solution of from inspiring English sources

where r ( t ) is the maximal solution of (3.5).

where ω is the maximal solution of the Cauchy problem (25).

Assume, for any η ∈ M ˜, the uniqueness of the maximal solution of problem (2.3).

Moreover, (eta(t)) is the maximal solution of (2.2) existing in ((0,+infty)).

where r t, τ 0, u 0) is the maximal solution of comparison equation (3.1.2).

Similarly, it is easy to verify that x ∗ ≤ x ˆ ∗, where x ∗ denotes the maximal solution of PBVP (1.1) in [ y, z ] and x ˆ ∗ is the maximal solution of PBVP (3.25) in [ y, z ]. □.

The maximal solutions of the optimization problem (1) are the so-called maximum likelihood estimators of the two Weibull parameters.

Then, there exist monotone sequences with such that uniformly on, and are the minimal and the maximal solutions of (1.1), respectively, such that.

The function (u^(t)=u(t t_{0},u_{0})), (u^in C^{q}([t_{0},T],mathbb{R})), is the maximal solution (minimal solution) of the initial value problem (5).

Consequently, for any ∈ W, the maximal solution x of (3.3) corresponding to is such that | ( x ′ ( t ) | = | λ f ( t, x t | ≤ | λ | c for all t ∈ [ 0, T ].

For the existence of the maximal solution (ymapsto g_ y)) of (4), note that the right-hand side of (4) is nondecreasing in (g(cdot)) provided that (H^{prime}(cdot)>0).