## A criterion for correct solvability of the Sturm-Liouville equation in the space $L_{p}(R)$

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- by N. Chernyavskaya and L. Shuster
- Proc. Amer. Math. Soc.
**130**(2002), 1043-1054 - DOI: https://doi.org/10.1090/S0002-9939-01-06145-7
- Published electronically: September 14, 2001
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## Abstract:

We consider an equation \begin{equation}\tag {1} -y''(x) + q(x)\ y(x) = f(x),\qquad x\in R, \end{equation} where $f(x) \in L_{p}(R),\ p\in [1,\infty ]\ \left (\| f \|_{\infty } := C (R) \right )$, and $0 \le q(x)\in L_{1}^{\operatorname {loc}} (R).$ By a solution of equation (1), we mean any function $y(x)$ such that $y(x), yâ(x) \in AC^{\operatorname {loc}} (R),$ and equality (1) holds almost everywhere on $R.$ In this paper, we obtain a criterion for the correct solvability of (1) in $L_{p} (R)$, $p \in [1,\infty ].$## References

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## Bibliographic Information

**N. Chernyavskaya**- Affiliation: Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, 84105, Israel
**L. Shuster**- Affiliation: Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israel
- Received by editor(s): April 6, 2000
- Received by editor(s) in revised form: October 4, 2000
- Published electronically: September 14, 2001
- Additional Notes: This research was supported by the Israel Academy of Sciences under Grant 431/95
- Communicated by: Carmen C. Chicone
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**130**(2002), 1043-1054 - MSC (2000): Primary 34C11, 34B40, 47E05
- DOI: https://doi.org/10.1090/S0002-9939-01-06145-7
- MathSciNet review: 1873778