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We consider an equation (1) -y(x) + q(x) y(x) = f(x), x ∈ R, where f(x) ∈ L p (R), p ∈ [1,∞] (∥f∥∞:= C(R)), and 0 ≤ q(x) ∈ L loc 1 (R). By a solution of equation (1), we mean any function y(x) such that y(x), y' (x) E AC loc (R), and equality (1) holds almost everywhere on R. In this paper, we obtain a criterion for the correct solvability of (1) in Lp(R), p E [1,∞].

A criterion for correct solvability of the Sturm-Liouville equation in the space 𝐿_{𝑝}(𝑅)