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

Ospanov, Kordan Naurzykanovič: Maximal Lp-regularity for a second-order differential equation with unbounded intermediate coefficient. Electronic journal of qualitative theory of differential equations 65. pp. 1-13. (2019)

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Abstract

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 (−∞, +∞).

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 65
Page Range: pp. 1-13
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.65
Uncontrolled Keywords: Másodrendű differenciálegyenlet
Additional Information: Bibliogr.: p. 11-13. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 30. 11:35
Last Modified: 2019. Sep. 30. 11:35
URI: http://acta.bibl.u-szeged.hu/id/eprint/62289

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