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

  • N.A. Chernyavskaya

    Ben Gurion University of the Negev, Beer-Sheba, Israel
  • L.A. Shuster

    Bar-Ilan University, Ramat-Gan, Israel

Abstract

We consider the singular boundary value problem

where , (, is a continuous positive function on , . A solution of this problem is, by definition, any absolutely continuous function satisfying the limit condition and almost everywhere the differential equation. This problem is called correctly solvable in a given space if for any function it has a unique solution and if the following inequality holds with an absolute constant

We find minimal requirements for and under which the above problem is correctly solvable in .

Cite this article

N.A. Chernyavskaya, L.A. Shuster, 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