Abstract
AbstractIn this paper, we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations $$\begin{aligned} A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} 0, \\ A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} F, \end{aligned}$$
A
k
(
z
)
f
(
z
+
c
k
)
+
⋯
+
A
1
(
z
)
f
(
z
+
c
1
)
+
A
0
(
z
)
f
(
z
)
=
0
,
A
k
(
z
)
f
(
z
+
c
k
)
+
⋯
+
A
1
(
z
)
f
(
z
+
c
1
)
+
A
0
(
z
)
f
(
z
)
=
F
,
where $$A_{k}\left( z\right) ,\ldots ,A_{0}\left( z\right) ,$$
A
k
z
,
…
,
A
0
z
,
$$F\left( z\right) $$
F
z
are meromorphic functions and $$c_{j}$$
c
j
$$\left( 1,\ldots ,k\right) $$
1
,
…
,
k
are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng, Belaïdi and Benkarouba.
Publisher
Springer Science and Business Media LLC
Reference21 articles.
1. Belaïdi, B.; Benkarouba, Y.: Some properties of meromorphic solutions of higher order linear difference equations. Ser. A Appl. Math. Inform. Mech. 11(2), 75–95 (2019)
2. Cao, T.B.; Xu, J.F.; Chen, Z.X.: On the meromorphic solutions of linear differential equations on the complex plane. J. Math. Anal. Appl. 364(1), 130–142 (2010)
3. Chiang, Y.M.; Feng, S.J.: On the Nevanlinna characteristic of $$f\left( z+\eta \right) $$ and difference equations in the complex plane. Ramanujan J. 16(1), 105–129 (2008)
4. Goldberg, A., Ostrovskii, I.: Value Distribution of Meromorphic functions. Transl. Math. Monogr., vol. 236, Amer. Math. Soc., Providence (2008)
5. Halburd, R.G.; Korhonen, R.J.: Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J. Math. Anal. Appl. 314(2), 477–487 (2006)
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