On an Invertible Extension of a Nonself-Adjoint Singular Differential Operator on the Half-Line

We consider the differential operator generated in the class of compactly supported functions on the positive half-line by the nonself-adjoint differential expression with locally Lebesgue integrable coefficients. Cases are not excluded where ( ) are sign-alternating or can have infinite limits as (with any sign). Descriptions of the internal connections between the coefficients ( ) are given under which the operator in question admits a closed invertible extension in the space .