## A singularly perturbed linear system in a critical case.(Russian)Zbl 0641.34058

The author considers an initial value problem for a system of singularly perturbed linear ordinary differential equations $\frac{dx}{dt}=A_{11}(t)x(t)+A_{12}(t)y(t)+f(t)$
$\epsilon \frac{dy}{dt}=A_{21}(t)x(t)+A_{22}(t)y(t)+g(t)$ where x,y,f,g are vector valued functions and $$A_{ik}$$ appropriate matrices. He proves the convergence of the asymptotic solution relaxing the usual condition that the stationary point of the equation $$\epsilon dy/dt=A_{22}(t)y(t)$$ is asymptotically stable.
Reviewer: J.Miko

### MSC:

 34E15 Singular perturbations for ordinary differential equations 35A35 Theoretical approximation in context of PDEs