Sentence examples for mild solution to from inspiring English sources

We prove that the Feynman Kac representation(1)u t,x)="Ex[uo(X t))exp⁡∫0tW(ds,X(t−s))], is a mild solution to this problem.

Then there exists a unique (local) continuous mild solution to (1.1) for any initial value.

Hence, ϕ is a piecewise pseudo almost periodic mild solution to Eq. (1.1).

That is, the exponential stability in -moment for mild solution to system (2.1) is obtained.

Following [22, 23] we will introduce now the definition of mild solution to (1.1).

Consequently, by Theorem 3.1, there exists a unique mild solution to Eq. (33).

However, one cannot ensure the unique existence of almost automorphic mild solution to (2.26) when (2.32).

From Theorem 3.5 it follows that (X_{s}) is a mild solution to Eq. (3.15).

We examine asymptotically almost periodic mild solution to the fractional relaxation-oscillation equation given by.

We first introduce the notion of mild solution to system (1.1 - 1.2 1.1 - 1.2

By Lemma 3.1 we define a mild solution to problem (3.1) as follows.