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2000 Linearized stability for semilinear non-autonomous evolution equations with applications to retarded differential equations
Gabriele Gühring, Wolfgang M. Ruess, Frank Räbiger
Differential Integral Equations 13(4-6): 503-527 (2000).

Abstract

We consider the semilinear non-autonomous evolution equation $\frac{d}{dt}u(t)=Au(t)+G(t,u(t))$, $t\geq s\geq 0,$ where $(A,D(A))$ is a Hille-Yosida operator on a Banach space $X$ and $G$ is a continuous function on $\mathbb R_+\times \overline{D(A)}$ with values in the extrapolated Favard class corresponding to $A$. In our main results we present principles of linearized stability and instability for a solution of such an equation. Our approach is based on the theory of extrapolation spaces. We apply the results to non-autonomous semilinear retarded differential equations.

Citation

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Gabriele Gühring. Wolfgang M. Ruess. Frank Räbiger. "Linearized stability for semilinear non-autonomous evolution equations with applications to retarded differential equations." Differential Integral Equations 13 (4-6) 503 - 527, 2000.

Information

Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 0990.34068
MathSciNet: MR1750038

Subjects:
Primary: 34G20
Secondary: 34K30, 35B35, 47D06

Rights: Copyright © 2000 Khayyam Publishing, Inc.

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Vol.13 • No. 4-6 • 2000
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