Abstract
In this paper, we study the existence of solutions for integrodifferential Stein–Weiss equations of the form
−
L
K
u
+
V
(
x
)
u
=
1
|
x
|
β
(
∫
R
F
(
y
,
u
(
y
)
)
|
y
−
x
|
μ
|
y
|
β
d
y
)
f
(
x
,
u
(
x
)
)
,
in
R
,
where
μ
>
0
,
β
≥
0
such that
0
μ
+
2
β
1
,
−
L
K
is a nonlocal operator with a measurable kernel which satisfies "structural properties", more general than the standard kernel of the fractional Laplacian operator,
V
is a bounded potential which can change sign, the nonlinear term
f
(
x
,
u
)
has the critical exponential growth with respect to the Trudinger–Moser inequality and
F
(
x
,
t
)
=
∫
0
t
f
(
x
,
s
)
d
s
.