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Connections between Hyers and Lyapunov stability of the ordinary differential equations. (English) Zbl 1159.34332
Summary: We consider two kinds of stability of the differential equation \(x'=f(t,x)\) where \(f:\mathbb R^2\to\mathbb R\) is a continuous function, Lipschitzian with respect to the second variable. We prove that the Hyers stability implies the one in the sense of Lyapunov whereas the converse is not true.

MSC:
34D20 Stability of solutions to ordinary differential equations
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