AbstractWe study the following Choquard type equation in the whole plane $$\begin{aligned} (C)\quad -\Delta u+V(x)u=(I_2*F(x,u))f(x,u),\quad x\in \mathbb {R}^2 \end{aligned}$$
(
C
)
-
Δ
u
+
V
(
x
)
u
=
(
I
2
∗
F
(
x
,
u
)
)
f
(
x
,
u
)
,
x
∈
R
2
where $$I_2$$
I
2
is the Newton logarithmic kernel, V is a bounded Schrödinger potential and the nonlinearity f(x, u), whose primitive in u vanishing at zero is F(x, u), exhibits the highest possible growth which is of exponential type. The competition between the logarithmic kernel and the exponential nonlinearity demands for new tools. A proper function space setting is provided by a new weighted version of the Pohozaev–Trudinger inequality which enables us to prove the existence of variational, in particular finite energy solutions to (C).