A remark on the Lyapunov-Razumikhin method for equations with infinite delay
The system of functional-differential equations \[ \frac{dx}{dt}=X(t,x_t)\tag{1} \] is considered. It is assumed that this system has the zero solution \(x(t)=0\). Using some properties of the limit equation \[ \frac{dx}{dt}=X_*(t,x_t), \] the author obtains sufficient conditions for the asymptotic stability of the zero solution to system (1).
differential equations with infinite delay
scientific article; zbMATH DE number 1916191
scientific article