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A Global Existence Theorem for Autonomous Differential Equations in a Banach Space

R. H. Martin, Jr.
Proceedings of the American Mathematical Society
Vol. 26, No. 2 (Oct., 1970), pp. 307-314
DOI: 10.2307/2036395
Stable URL: http://www.jstor.org/stable/2036395
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Global Existence Theorem for Autonomous Differential Equations in a Banach Space
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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, ∞) 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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