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I. Rachunkova, S. Stanek, E. Weinmüller, M. Zenz:
"Limit properties of solutions os singular second-order differential equations";
in: "ASC Report 08/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

We discuss the properties of the differential equation
u′′(t) =
a
t
u′(t) + f(t, u(t), u′(t)), a.e. on (0, T],
where a ∈ R\{0}, and f satisfies the Lp-Carath´eodory conditions on [0, T]×R2 for
some p > 1. A full description of the asymptotic behavior for t → 0+ of functions
u satisfying the equation a.e. on (0, T] is given. We also describe the structure
of boundary conditions which are necessary and sufficient for u to be at least
in C1[0, T]. As an application of the theory, new existence and/or uniqueness
results for solutions of periodic boundary value problems are shown

singular problem; second-order differential equation; asymptotic

http://www.asc.tuwien.ac.at/preprint/2009/asc08x2009.pdf