Meromorphic Solutions of Nonlinear Differential-Difference Equations Involving Periodic Functions
We investigate the following two types of nonlinear differential-difference equations L ( z , f ) + H ( z , f ) = ∑ k = 1 r α k ( z ) e β k z ; L ( z , f ) + H ( z , f ) = ∑ k = 1 r F k ( z ) , where α 1 , … , α r are meromorphic functions of order < 1 , and F 1 , … , F r are periodic transcenden...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2024-05, Vol.47 (3), Article 91 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We investigate the following two types of nonlinear differential-difference equations
L
(
z
,
f
)
+
H
(
z
,
f
)
=
∑
k
=
1
r
α
k
(
z
)
e
β
k
z
;
L
(
z
,
f
)
+
H
(
z
,
f
)
=
∑
k
=
1
r
F
k
(
z
)
,
where
α
1
,
…
,
α
r
are meromorphic functions of order
<
1
,
and
F
1
,
…
,
F
r
are periodic transcendental entire functions, and
L
,
H
are defined by
L
(
z
,
f
)
=
∑
k
=
1
p
a
k
(
z
)
f
(
m
k
)
(
z
+
τ
k
)
≢
0
,
H
(
z
,
f
)
=
∑
k
=
1
q
b
k
(
z
)
[
f
(
n
k
)
(
z
+
ζ
k
)
]
s
k
with small meromorphic coefficients
a
i
,
b
j
.
By introducing a new method, we obtain the exact forms of the solutions of these two equations under certain growth conditions. |
|---|---|
| ISSN: | 0126-6705 2180-4206 |
| DOI: | 10.1007/s40840-024-01681-9 |