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Second order linear differential equations of Fuchsian type with four singularities. (English) Zbl 1049.34107
The paper deals with the second-order linear differential equation $y''+p(x)y'+q(x)y = 0,$ where $$p(x)$$ and $$q(x)$$ are arbitrary analytic functions. The author proposes a change of variables to decompose the system into two subsystems: an ordinary differential equation on the central manifold and integral equations on the stable manifold.
##### MSC:
 34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
##### Keywords:
equations of Fuchsian type; singularities