Abstract
AbstractIn this paper, we investigate the non-existence of transcendental entire solutions for non-linear differential-difference equations of the forms $$\begin{aligned} f^{n}(z)+Q(z,f)=\beta _{1}e^{\alpha _{1}z}+\beta _{2}e^{\alpha _{2}z}+\cdots +\beta _{s}e^{\alpha _{s}z} \end{aligned}$$
f
n
(
z
)
+
Q
(
z
,
f
)
=
β
1
e
α
1
z
+
β
2
e
α
2
z
+
⋯
+
β
s
e
α
s
z
and $$\begin{aligned} f^{n}(z)f^{(k)}(z)+L_d(z,f)=\sum ^{s}_{i=1}p_i(z)e^{\alpha _i{(z)}}, \end{aligned}$$
f
n
(
z
)
f
(
k
)
(
z
)
+
L
d
(
z
,
f
)
=
∑
i
=
1
s
p
i
(
z
)
e
α
i
(
z
)
,
where n, s are positive integers, $$n\ge s+2,$$
n
≥
s
+
2
,
Q(z, f) is a differential-difference polynomial in f of degree d.
Funder
Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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