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We consider the equation
where 
and
We 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 
. Here
In the case p = 2, for the compact operator 
, we obtain two-sided sharp-by-order estimates of the maximal eigenvalue.
