Sentence examples for be the mild solution from inspiring English sources

Let X ( t ) be the mild solution of (2.1).

Let x be the mild solution of Cauchy problem (3.1).

Let be the mild solution of (2.12 - 2.13) and assume that.

Let (x cdot)) be the mild solution of (1.1) given by (3.2).

The function (x : [0, a] to X) given by (3.20) is said to be the mild solution of problem (1.1 - 1.2 1.1 - 1.2

for any φ ∈ D ( L ) ∩ C b 1 ( H ). Proof Let X ( t, x ) be the mild solution of (1.1) and Z ( t, x ) be the mild solution of (3.2), for any φ ∈ D ( L ) ∩ C b 1 ( H ), taking into account that X ( t, x ) = Z ( t, x ) + ∫ 0 t e ( t − s ) A F ( X ( s, x ) ) d s + ∫ 0 t e ( t − s ) A ( G ( X ( s, x ) ) − G ( Z ( s, x ) ) ) d W ( s ), by the Taylor formula we have ℙ-a.s.s

We know that the fixed point of Φ is the mild solution of problem (1.1).

It is easy to notice that the fixed point of (mathcal{O}) is the mild solution of problem (2).

It is easy to see that the fixed point of (Phi_{n}) is the mild solution of problem (3.2 - 3.4 3.2 - 3.4

It is easy to see that the fixed point of K is the mild solution of nonlocal impulsive problem (1.1).

Therefore F has at least one fixed point x in  Q ∞, which is the mild solution of problem (1.1).