A global existence theorem for a nonautonomous differential equation in a Banach space
A global existence theorem for a nonautonomous differential equation in a Banach space
Suppose that <italic>X</italic> is a real or complex Banach space and that <italic>A</italic> is a continuous function from <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket 0 comma normal infinity right-parenthesis times upper X"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>×</mml:mo> <mml:mi>X</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">[0,\infty ) \times X</mml:annotation> </mml:semantics> …