Maximal $L_{p} $-regularity for a second-order differential equation with unbounded intermediate coefficient

We consider the following equation \[-y''+r\left(x\right)y'+q\left(x\right)y=f(x), \] where the intermediate coefficient $r$ is not controlled by $q$ and it is can be strong oscillate. We give the conditions of well-posedness in $L_{p} \left(-\infty ,\, +\infty \right)$ of this equation. For the solution $y$, we obtained the following maximal regularity estimate: \[\left\| y''\right\| _{p} +\left\| ry'\right\| _{p} +\left\| qy\right\| _{p} \le C\left\| f\right\| _{p} ,\] where $\left\| \, \cdot \, \right\| _{p} $ is the norm of $L_{p} \left(-\infty ,\, +\infty \right)$