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

Abstract

We consider the equationwhere andWe assume that this equation is correctly solvable in Lp(ℝ). Under these assumptions, we study the problem of compactness of the resolvent of the maximal continuously invertible Sturm–Liouville operator . HereIn the case p = 2, for the compact operator , we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.