Sentence examples for mild solution in from inspiring English sources

(v) is the unique bounded mild solution in of.

Then Eq. (4.1) has a unique mild solution in (mathit{PAA}(mathbb{X},mu)).

holds, then we can obtain the uniqueness of the mild solution in Theorem 3.2.

Then (4.1) has a unique mild solution in (WPAP mathbb{R},X)).

has at least one mild solution in (C^{nu,mu }(J,E)).

Besides, if (f t,theta)neqtheta), the unique mild solution in (B(J,E)) is nontrivial.

We shall study the existence and approximation of mild solutions in the following sense.

Then the IVP (1.1) has minimal and maximal mild solutions in C J, X. Proof.

Some sufficient conditions ensuring the exponential decay of mild solutions in the pth moment to the stochastic systems are obtained.

We will use Lemma 1 to prove that the fractional nonlocal evolution equation (3.5) has a mild solutions in X.

Precisely, Liu [11] considered a linear neutral stochastic differential equations with constant delays and some stability properties of the mild solutions in a similar way as Datko [25] in the deterministic case.