Maximal Lp-regularity for a second-order differential equation with unbounded intermediate coefficient

We consider the following equation −y 00 + r (x) y 0 + q (x) 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 Lp (−∞, +∞) of this equation. For the solution y, we obtained the following maximal regularity estimate: y 00 p + ry0 p + kqykp ≤ C k f kp where k · kp is the norm of Lp (−∞, +∞)