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. Linearized equation: $$ y' = Ay + f. $$ If all eigenvalues $\lambda(A)$ are such that $\mathrm{Re}\,\lambda(A) \leq -\sigma_0 < 0$, then the solution is stable.
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$\begingroup$ Try this if you can get it :dynamicsystems.asmedigitalcollection.asme.org/… $\endgroup$– zeraoulia rafikCommented Jan 6, 2017 at 21:02
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