A. Feichtinger, I. Rachunkova, S. Stanek, E. Weinmüller:

"Periodic BVPs in ODEs with time singularities";

in: "ASC Report 04/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

In this paper we show the existence of solutions to a nonlinear singular

second order ordinary differential equation,

u′′(t) =

a

t

u′(t) + f(t, u(t), u′(t)),

subject to periodic boundary conditions, where a > 0 is a given constant, > 0

is a parameter, and the nonlinearity f(t, x, y) satisfies the local Carathéodory

conditions on [0, T] × R × R. Here, we study the case that a well-ordered

pair of lower and upper functions does not exist and therefore the underlying

problem cannot be treated by well-known standard techniques. Instead, we

assume the existence of constant lower and upper functions having opposite

order. Analytical results are illustrated by means of numerical experiments.

Singular boundary value problems, periodic boundary conditions,

http://www.asc.tuwien.ac.at/preprint/2011/asc04x2011.pdf

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