Golokvoschyus, P. B. Asymptotic estimates of the norm of the integral matrix of a two-dimensional system of differential equations in the neighborhood of a singular point of the system. (Russian) Zbl 0569.34049 Differ. Uravn. 21, No. 2, 325-328 (1985). Let Y(\(\tau)\) be the solution matrix of the second order matrix differential equation \(dY/d\tau =Y(A\tau^{-2}+B\tau^{\mu -2})\) where \(A=-\left( \begin{matrix} \xi_ 1&0\\ 1&\xi_ 2\end{matrix}\right)\), \(B=- \left( \begin{matrix} \eta_ 1&\nabla\\ 0&\eta_ 2\end{matrix}\right)\) \(\xi_ i\), \(\eta_ i\) and \(\nabla\) being complex numbers, \(\mu \in (0,+\infty)\) and \((\xi_ 2-\xi_ 1)(\eta_ 2-\eta_ 1)+\nabla \neq 0,\) \(\nabla \neq 0\). For \(\tau\) \(\to \infty\) the following asymptotic behaviour is proved \(| Y(\tau)| \leq a\cdot e^{-c}\), \(\mu\in (0,1)\), \(| Y(\tau)| =O(\tau^ k)\), \(\eta =0\), \(| Y(\tau)| =O(\exp (c\tau^{\mu -1})),\) \(\mu \in (1,+\infty)\) where a,\(\kappa\),c, are numbers that can be computed by explicit formulae using the coefficients \(\xi_ i\), \(\eta_ i\), \(\nabla\). Reviewer: V.Răsvan MSC: 34E05 Asymptotic expansions of solutions to ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34A30 Linear ordinary differential equations and systems Keywords:solution matrix; second order matrix differential equation PDFBibTeX XMLCite \textit{P. B. Golokvoschyus}, Differ. Uravn. 21, No. 2, 325--328 (1985; Zbl 0569.34049)