Abstract
We consider the differential operator generated in the class of compactly supported functions on the positive half-line by the nonself-adjoint differential expression $${-a_{2}(x)}f^{\prime {}\prime }+a_{1}(x)f^{\prime }+a_{0}(x)f$$ with locally Lebesgue integrable coefficients. Cases are not excluded where $$a_{j}(x) $$ ( $$j = 0,1$$ ) are sign-alternating or can have infinite limits as $$x\to \infty $$ (with any sign). Descriptions of the internal connections between the coefficients $$a_{j} $$ ( $$j = 0,1,2$$ ) are given under which the operator in question admits a closed invertible extension in the space $$L_{2}(0,\infty ) $$ .