I am looking for a book on stability theory. More precisely, I am interested in the case of a system of differential equations $\frac{dx}{dt}=Ax + F(x),$ where $A$ is a constant matrix, such that two of its eigenvalues have zero real parts and other eigenvalues have negative real parts. Where can I read Lyapunov's results on when the zero solution is stable?
Book on stability theory
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reference-request
ordinary-differential-equations
1 Answers
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There is a detailed discussion of these problems in "Geometrical methods in the theory of ODE" by V.I.Arnold, though I think this is much more general than what you're looking for.
So I recommend two other books of the same author, "Ordinary differential equations" and "Advanced chapters in theory of ODE".