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

 

A principle of linearized stability for nonlinear evolution equations


Author: Nobuyuki Kato
Journal: Trans. Amer. Math. Soc. 347 (1995), 2851-2868
MSC: Primary 34G20; Secondary 34D05, 34K30, 35K55, 47N20
MathSciNet review: 1290722
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Abstract: We present a principle of linearized stability of stationary solutions to nonlinear evolution equation in Banach spaces. The well-known semilinear case is shown to fit into our framework. Applications to nonlinear population dynamics and to functional differential equations are also considered.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1290722-8
PII: S 0002-9947(1995)1290722-8
Keywords: Linearized stability, $ m$-accretive operators, proto-derivatives, nonlinear evolution equations, population dynamics, functional differential equations
Article copyright: © Copyright 1995 American Mathematical Society