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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
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