Transformation of a singular boundary-value problem on a half-line to an integral equation with a discontinuous operator

A. I. Kolosov

Khar'kov Institute of Communal-Construction Engineers

Abstract: An investigation of a boundary-value problem on a half-line for a nonlinear ordinary second-order differential equation whose free term has a discontinuity in a strip. A method is proposed for the transformation of the boundary-value problem into an integral equation with a discontinuous operator. Some results have recently been obtained concerning the existence, the comparison, and integral representations of solutions of this integral equation.

UDC: 517

Received: 22.10.1969

 English version: Mathematical Notes, 1971, 9:1, 45–48

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