We consider an equation
(1)
−
y
(
x
)
+
q
(
x
)
y
(
x
)
=
f
(
x
)
,
x
∈
R
,
\begin{equation}\tag {1} -y(x) + q(x)\ y(x) = f(x),\qquad x\in R, \end{equation}
where
f
(
x
)
∈
L
p
(
R
)
,
p
∈
[
1
,
∞
]
(
‖
f
‖
∞
:=
C
(
R
)
)
f(x) \in L_{p}(R),\ p\in [1,\infty ]\ \left (\| f \|_{\infty } := C (R) \right )
, and
0
≤
q
(
x
)
∈
L
1
loc
(
R
)
.
0 \le q(x)\in L_{1}^{\operatorname {loc}} (R).
By a solution of equation (1), we mean any function
y
(
x
)
y(x)
such that
y
(
x
)
,
y
′
(
x
)
∈
A
C
loc
(
R
)
,
y(x), y’(x) \in AC^{\operatorname {loc}} (R),
and equality (1) holds almost everywhere on
R
.
R.
In this paper, we obtain a criterion for the correct solvability of (1) in
L
p
(
R
)
L_{p} (R)
,
p
∈
[
1
,
∞
]
.
p \in [1,\infty ].