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 regula...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Másodrendű differenciálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.65 |
| Online Access: | http://acta.bibl.u-szeged.hu/62289 |
| Tartalmi kivonat: | 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 (−∞, +∞). |
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| Terjedelem/Fizikai jellemzők: | 1-13 |
| ISSN: | 1417-3875 |