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Contributions to Books:

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.



English abstract:
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.

Keywords:
Singular boundary value problems, periodic boundary conditions,


Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2011/asc04x2011.pdf


Created from the Publication Database of the Vienna University of Technology.