On the Generalized Solution of the Boundary-Value Problem for the Operator-Differential Equations of the Second Order with Variable Coefficients

Abstract

Boundary-value problem for a class of operator-differential equations of the second order with variable coefficients on [0;+∞) is studied. The principal part of investigated operator-differential equation has discontinuities. Sufficient conditions for the existence and uniqueness of generalized solutions of the boundary-value problem for such equations are given. These conditions are expressed only in terms of coe cients of the operator-differential equation.