Correct solvability, embedding theorems and separability for the Sturm-Liouville equation

被引：0
|
作者：
Chernyavskaya N.A. [1 ]
Shuster L.A. [2 ]
机构：
[1] Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva
[2] Department of Mathematics, Bar-Ilan University, Ramat Gan
来源：
Bollettino dell'Unione Matematica Italiana | 2015年 / 8卷 / 1期
关键词：
Embedding theorem; Sobolev space; Sturm-Liouville equation;
D O I：
10.1007/s40574-015-0024-2
中图分类号：
学科分类号：
摘要：
For p [1,∞), f Lp(ℝ) and 0 ≤ q L1Loc(ℝ), we show that the weighted function space S(2)p (R, q) ={ y AC(1)loc (ℝ) : ∥y" qy∥p + ∥q1/p y∥p < ∞} is embedded into L p(R) if and only if the equation -y"(x) + q(x)y(x) = f (x), x ℝ, is correctly solvable in Lp(ℝ). © Unione Matematica Italiana 2015.
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页码：45 / 52
页数：7
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