On Generalized Solutions of Some Differential Equations with Singular Coefficients

Abstract

The article deals with the problem of existence of generalized solutions to simplest linear differential equation with a singular coefficient q. The generalized solution was introduced by choice one of the distribution Q corresponding q, and choice an approximation of Q by a family of common functions. The generalized solution is defined as the limit of the solutions of the approximating equations. It was demonstrated by model example that the existence of such generalized solutions depends essentially on the method of approximation.