Abstract
In this paper, we study the existence and nonexistence of positive bounded solutions of the integral equation
u
=
λ
V
(
a
f
(
u
)
)
, where
λ
is a positive parameter,
a
is a nontrivial nonnegative measurable function with bounded potential and
V
belongs to a class of positive kernels that contains in particular the potential kernel of the classical Laplacian
V
=
(
−
Δ
)
−
1
or
V
=
(
∂
∂
t
−
Δ
)
−
1
or the inverse of the polyharmonic Laplacian
(
−
Δ
)
m
,
m
≥
2
.