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) =
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,

Electronic version of the publication:

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