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Journal of the London Mathematical Society Advance Access published online on May 19, 2009
Journal of the London Mathematical Society, doi:10.1112/jlms/jdp012
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© 2009 London Mathematical Society

A criterion for correct solvability in Lp(R) of a general Sturm–Liouville equation

N. Chernyavskaya

Department of Mathematics and Computer Science
Ben-Gurion University of the Negev
P.O.B. 653
Beer-Sheva 84105
Israel
nina@math.bgu.ac.il

L. Shuster

Department of Mathematics
Bar-Ilan University
Ramat Gan 52900
Israel

We consider an equation


Formula

where f isin Lp(R) for p isin (1, {infty}) with the following conditions:


Formula

By a solution of the above-mentioned equations, we mean any function y that is absolutely continuous together with ry' and satisfies it almost everywhere on R. Under the above-mentioned conditions, we give a criterion for the correct solvability of the above-mentioned equation in Lp(R) for p isin (1, {infty}).

2000 Mathematics Subject Classification 34B24, 34L40.

Received February 26, 2008; revised January 21, 2009;
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