# Conditions for Correct Solvability of a Simplest Singular Boundary Value Problem of General Form. I

### L.A. Shuster

Bar-Ilan University, Ramat-Gan, Israel### N.A. Chernyavskaya

Ben Gurion University of the Negev, Beer-Sheba, Israel

## Abstract

We consider the singular boundary value problem

where $f∈L_{p}(R)$, $p∈[1,∞]$ ($L_{∞}(R):=C(R))$, $r$ is a continuous positive function on $R$, $0≤q∈L_{1}$. A solution of this problem is, by definition, any absolutely continuous function $y$ satisfying the limit condition and almost everywhere the differential equation. This problem is called correctly solvable in a given space $L_{p}(R)$ if for any function $f∈L_{p}(R)$ it has a unique solution $y∈L_{p}(R)$ and if the following inequality holds with an absolute constant $c_{p}∈(0,∞):$

We find minimal requirements for $r$ and $q$ under which the above problem is correctly solvable in $L_{p}(R)$.

## Cite this article

L.A. Shuster, N.A. Chernyavskaya, Conditions for Correct Solvability of a Simplest Singular Boundary Value Problem of General Form. I. Z. Anal. Anwend. 25 (2006), no. 2, pp. 205–235

DOI 10.4171/ZAA/1285