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On the compactness of the evolution operator generated by certain nonlinear $ \Omega$-accretive operators in general Banach spaces

Author: Athanassios G. Kartsatos
Journal: Proc. Amer. Math. Soc. 123 (1995), 2081-2091
MSC: Primary 47H20; Secondary 34G20, 39B72, 47H06
MathSciNet review: 1307535
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Abstract: A sufficient condition is given for the compactness of the evolution operator $ U(t,s)$ generated by a family of nonlinear $ \omega $-accretive operators $ A(t)$. This family $ A(t)$ satisfies a time-dependence condition which is not covered by the results of Calvert and the author. It is also shown that the main part of this sufficient condition is necessary.

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Keywords: Compact evolution operator, $ \omega $-accretive operator, compact resolvents, Crandall-Pazy theory
Article copyright: © Copyright 1995 American Mathematical Society

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