Here, we consider an anisotropic equation
\[
−
Δ
H
n
,
p
→
u
+
a
(
q
)
|
u
|
p
–
2
u
=
λ
w
(
q
)
|
u
|
m
−
2
u
−
h
(
q
)
|
u
|
l
−
2
u
,
-\Delta _{{\mathbb {H}^n},\overrightarrow {p}}u +a(q)|u|^{p^–2}u=\lambda w(q)|u|^{m-2}u-h(q)|u|^{l-2}u,
\]
in the Heisenberg group
H
n
{\mathbb {H}^n}
, where the operator
Δ
H
n
,
p
→
\Delta _{{\mathbb {H}^n},\overrightarrow {p}}
is the horizontal anisotropic
p
p
-Laplacian on the Heisenberg group and is defined in the sequel. By the variational methods, we prove the existence of the entire weak solutions.