Second order linear differential equations of Fuchsian type with four singularities. (English) Zbl 1049.34107

Lukashevich, N. A.

Nonlinear Oscil. 4, No. 3, 308-315 (2001).

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.

Reviewer: R. K. Azimov (Andizhan)

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