On essential self-adjointness of singular Sturm-Liouville operators

Considering singular Sturm–Liouville differential expressions of the type τα = −(d/dx)x (d/dx) + q(x), x ∈ (0, b), α ∈ R, we employ some Sturm comparison-type results in the spirit of Kurss to derive criteria for τα to be in the limit point and limit circle case at x = 0. More precisely, if α ∈ R and for 0 < x sufficiently small, q(x) ≥ [(3/4) − (α/2)]x, or, if α ∈ (−∞, 2) and there exist N ∈ N, and ε > 0 such that for 0 < x sufficiently small, q(x) ≥ [(3/4) − (α/2)]x − (1/2)(2 − α)x N ∑