  We consider the equation
  \begin{equation} -y''(x)+q(x)y(x)=f(x),\quad x\in \mathbb R
  \end{equation}
  where $ f \in L_p^{loc}(\mathbb R),$ $p \in [1,\infty) $ and $ 0 < q \in
L_1^{loc}(\mathbb R).$ By a solution of this equation we mean any function $
y,$ absolutely continuous together with its derivative and satisfying the
equation almost everywhere in $ \mathbb R.$ Let positive and continuous
functions $ \mu(x) $ and $ \theta(x) $ for $ x \in \mathbb R $ be given. Let us
introduce the spaces
  $ L_p(\mathbb R,\mu) = \{f \in L_p^{loc}(\mathbb R): ||f||_{L_p(\mathbb
R,\mu)}^p =\int_{-\infty}^\infty|\mu(x)f(x)|^p dx < \infty\}, $
  $ L_p(\mathbb R,\theta) = \{f\in L_p^{loc}(\mathbb R):||f||_{L_p(\mathbb
R,\theta)}^p = \int_{-\infty}^\infty|\theta(x)f(x)|^p dx < \infty\}. $
  In the present paper, we obtain requirements to the functions $\mu,\theta$
and $q$ under which
  1) for every function $f \in L_p(\mathbb R,\theta) $ there exists a unique
solution of the equation $y \in L_p(\mathbb R,\mu)$ ;
  2) there is an absolute constant $ c(p) \in (0,\infty) $ such that regardless
of he choice of a function $ f \in L_p(\mathbb R,\theta) $ the solution of the
equation satisfies the inequality
  $$ \|y\|_{L_p(\mathbb R,\mu)} < c(p)\|f\|_{L_p(\mathbb R,\theta)}. $$
