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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
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