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.


34D20 Stability of solutions to ordinary differential equations