A global existence theorem for autonomous differential equations in a Banach space

Martin, R. H.

doi:10.1090/S0002-9939-1970-0264195-6

A global existence theorem for autonomous differential equations in a Banach space

Author: R. H. Martin
Journal: Proc. Amer. Math. Soc. 26 (1970), 307-314
MSC: Primary 34.95; Secondary 34.04
DOI: https://doi.org/10.1090/S0002-9939-1970-0264195-6
MathSciNet review: 0264195
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Abstract: Let $E$ be a Banach space and let $A$ be a continuous function from $E$ into $E$. Sufficient conditions are given to insure that the differential equation $u’(t) = Au(t)$ has a unique solution on $[0,\infty )$ for each initial value in $E$. One consequence of this result is that if $-A$ is monotonic, then $-A$ is $m$-monotonic and $A$ is the generator of a nonexpansive semigroup of operators.

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