A criterion for correct solvability of the Sturm-Liouville equation in the space <IMG >期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A criterion for correct solvability of the Sturm-Liouville equation in the space

Authors:	N. Chernyavskaya L. Shuster

Affiliation:	Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, 84105, Israel L. Shuster ; Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israel

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

Keywords:	Correct solvability Sturm-Liouville equation

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