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J. Burkotova, I. Rachunkova, E. Weinmüller:
"On singular BVPs with unsmooth data. Part 1: Analysis of the linear case with variable coefficient matrix";
in: "ASC Report 20/2015", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, 1 - 22.

In this paper, analytical properties of systems of singular linear or-
dinary differential equations with variable coefficient matrices and unsmooth inhomogeneities are investigated. The aim is to precisely formulate conditions which are necessary and/or sufficient for the existence and uniqueness of solutions which are at least continuous on the closed interval including the singular point. Smoothness properties of such solutions are also discussed. In the second part of the paper entitled - On singular BVPs with unsmooth data. Part 2: Convergence of the collocation schemes - the polynomial collocation is applied to solve the analytical problem and convergence properties are studied.

linear systems of ordinary differential equations, singular boundary value problems, time singularity of the first kind, unsmooth inhomogeneity

http://www.asc.tuwien.ac.at/preprint/2015/asc20x2015.pdf