Abstract
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).
Original language | English |
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Pages (from-to) | 45-52 |
Number of pages | 8 |
Journal | Bollettino dell'Unione Matematica Italiana |
Volume | 8 |
Issue number | 1 |
DOIs | |
State | Published - 8 Aug 2015 |
Keywords
- Embedding theorem
- Sobolev space
- Sturm-Liouville equation
ASJC Scopus subject areas
- General Mathematics