Sentence examples for mild solution is from inspiring English sources

We use the subvariant functional method to show that every K-minimizing mild solution is compact almost automorphic.

Moreover, exponential stability of the mild solution is established with sufficient conditions.

Furthermore, exponential stability of the mild solution is established under sufficient conditions.

Moreover, in Section 4, the continuous dependence of the mild solution is also investigated.

Next we show that this mild solution is continuously differentiable on [0, T'].

If (U_{0}in D mathcal{A})), then the above mild solution is a strong solution.

Sufficient conditions for the stability in the distribution of the mild solution are derived.

But, as pointed out by Hernández et al. in [14], some concepts of mild solution are not realistic; see, for examples, [6, 9, 10].

By applying the Banach fixed point theorem, the existence and uniqueness of mild solution are analytically proved in a Hilbert space.

By the Banach modified fixed point theorem in the selected intersection space, the existence and uniqueness of the global mild solution are obtained.

Under order conditions on the nonlinearity f, the asymptotic stability results of positive ω-periodic mild solution are obtained on R + by using operator semigroup theory and a monotone iterative technique.