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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Semigroups and stability of nonautonomous differential equations in Banach spaces


Author: Nguyen Van Minh
Journal: Trans. Amer. Math. Soc. 345 (1994), 223-241
MSC: Primary 34G10; Secondary 34D05, 34G20, 47D06, 47H20, 47N20
MathSciNet review: 1242785
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Abstract: This paper is concerned with nonautonomous differential equations in Banach spaces. Using the theory of semigroups of linear and nonlinear operators one investigates the semigroups of weighted translation operators associated with the underlying equations. Necessary and sufficient conditions for different types of stability are given in terms of spectral properties of the translation operators and the differential operators associated with the equations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1242785-2
PII: S 0002-9947(1994)1242785-2
Keywords: Weighted translation operator, semigroup, differential operator, uniform stability, exponential dichotomy, stability of individual solutions
Article copyright: © Copyright 1994 American Mathematical Society