Electron. J. Diff. Eqns., Vol. 2005(2005), No. 79, pp. 125.
Solutions approaching polynomials at infinity to nonlinear
ordinary differential equations
Christos G. Philos, Panagiotis Ch. Tsamatos
Abstract:
This paper concerns the solutions approaching polynomials at
to
th
order
()
nonlinear ordinary differential
equations, in which the nonlinear term depends on time
and on
, where
is the unknown function and
is an integer with
.
For each given integer
with
,
conditions are given which
guarantee that, for any real polynomial of degree at most
,
there exists a solution that is asymptotic at
to this
polynomial. Sufficient conditions are also presented for every
solution to be asymptotic at
to a real polynomial of
degree at most
.
The results obtained extend those by the
authors and by Purnaras [25] concerning the particular case
.
Submitted February 13, 2005. Published July 11, 2005.
Math Subject Classifications: 34E05, 34E10, 34D05
Key Words: Nonlinear differential equation; asymptotic properties;
asymptotic expansions; asymptotic to polynomials solutions.
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Christos G. Philos
Department of Mathematics
University of Ioannina
P. O. Box 1186, 451 10 Ioannina, Greece
email: cphilos@cc.uoi.gr 

P. Ch. Tsamatos
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: ptsamato@cc.uoi.gr 
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