Abstract:
We consider the following equation −y′′ + r (x) y′ + 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′′ ∥∥ p +∥∥ry′ ∥∥ p + ‖qy‖p ≤ C ‖ f ‖p, where ‖ · ‖p is the norm of Lp (−∞, +∞).
