Compactness Conditions for the Green Operator inLp(ℝ) Corresponding to a General Sturm-Liouville Operator

A criterion for compactness in L_p(R) of the resolvent of the maximal Sturm-Leovuile operator of general form

“…Remark 3.5. Theorems 3.1 and 3.4 were obtained in [5] under an additional requirement ϕ ≍ ψ(x), x ∈ R. The meaning of condition (3.1) can be clarified "in terms of the coefficients" of equation (1.1) in the same way as is done in Remark 2.26 for the interpretation of the condition B < ∞. In particular, in order to expand on Theorem 3.1, we state the following theorem.…”