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On a method for investigating systems of ordinary differential equations with singular points. (English. Russian original) Zbl 0841.34011
Russ. Acad. Sci., Dokl., Math. 49, No. 3, 454-459 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 336, No. 1, 21-24 (1994).
A method for constructing solutions of linear ODE systems of the form \[ xY'= A(x) Y+ F(x),\tag{1} \] where \(A(x)= (a_{ij}(x))^n_{i,j= 1}\), \(Y(x)= (y_1(x),\dots, y_n(x))\), \(F(x)= (f_1(x),\dots, f_n(x))\), is developed. Two propositions for constructing solutions “in a sufficiently small interval” of both nonhomogeneous and homogeneous systems (1) are proved. Sufficient conditions for the existence of a particular solution of systems (1) are obtained.
Reviewer: A.Dishliev (Sofia)
34A30 Linear ordinary differential equations and systems, general
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations