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Monomial summability and doubly singular differential equations
Ist Teil von
Journal of Differential Equations, 2007-02, Vol.233 (2), p.485-511
Ort / Verlag
Elsevier Inc
Erscheinungsjahr
2007
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
In this work, we consider systems of differential equations that are
doubly singular, i.e. that are both singularly perturbed and exhibit an irregular singular point. If the irregular singular point is at the origin, they have the form
ε
σ
x
r
+
1
d
y
d
x
=
f
(
x
,
ε
,
y
)
,
f
(
0
,
0
,
0
)
=
0
with
f analytic in some neighborhood of
(
0
,
0
,
0
)
. If the Jacobian
d
f
d
y
(
0
,
0
,
0
)
is invertible, we show that the unique bivariate formal solution is
monomially summable, i.e. summable with respect to the monomial
t
=
ε
σ
x
r
in a (new) sense that will be defined. As a preparation, Poincaré asymptotics and Gevrey asymptotics in a monomial are studied.