Example 4

Tag 08C1, permanent. Cite it as [Bourbaki, Tag 08C1].

Functions of a Real Variable, chapter IV, § 1. EXISTENCE THEOREMS

For the scalar equation $x' = \sin tx$ one has $I = H = \mathbf{R}$ and the right-hand side is bounded on $I \times H$ , so (IV, p. 173, cor. 1) every integral is defined on all of $\mathbf{R}$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Exercise 17, § 1

Cites

IV, p. 173