On continuity of the spectrum of a singular quasi-differential operator with respect to a parameter

Abstract

We obtain sufficient conditions for continuity of the eigenvalues of semi-bounded quasi-differential operators of order 2n on the half-axis with respect to the parameters that appear in the corresponding differential expression. In addition we obtain a generalization of the well-known result of M.G. Krein [9] concerning description of the quadratic form of a regular quasi-differential operator in the singular case, when the deficiency indices of the minimal operator are equal to (n,n).