A principle of linearized stability for nonlinear evolution equations

Kato, Nobuyuki

doi:10.1090/S0002-9947-1995-1290722-8

A principle of linearized stability for nonlinear evolution equations
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Trans. Amer. Math. Soc. 347 (1995), 2851-2868 Request permission

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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