A global existence theorem for a nonautonomous differential equation in a Banach space

Authors:
David Lowell Lovelady and Robert H. Martin

Journal:
Proc. Amer. Math. Soc. **35** (1972), 445-449

MSC:
Primary 34G05

DOI:
https://doi.org/10.1090/S0002-9939-1972-0303035-5

MathSciNet review:
0303035

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Abstract: Suppose that *X* is a real or complex Banach space and that *A* is a continuous function from into *X*. Suppose also that there is a continuous real valued function defined on such that is dissipative for each *t* in . In this note we show that, for each *z* in *X*, there is a unique differentiable function *u* from into *X* such that and for all *t* in . This is an improvement of previous results on this problem which require additional conditions on *A*.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0303035-5

Keywords:
Nonautonomous differential equations,
dissipative operators,
global existence theorems,
an application of nonlinear semigroups

Article copyright:
© Copyright 1972
American Mathematical Society