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I need some references concerning the asymptotic stability of eigenvalues by compact perturbations. In [T. Kato, Perturbation theory for linear operators] there are some results concerning stability ...

Where can I find a theorem about Lyapunov stability for the equation in Hilbert space? $$ y' = Fy, $$ where $F : V \to V'$ is a nonlinear operator , $y' \in L^2(0,T,V')$, $V$ is a Hilbert space. ...