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

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