Abstract: | We consider a boundary value problem where f(x) ∈ Lp(R), p ∈ [1,∞] (L∞(R) ≔ C(R) and 0 ≤ q(x) ∈ Lloc1( R). Boundary value problem (0.1) is called correctly solvable in the given space Lp(R) if for any f(x) ∈ Lp(R) there is a unique solution y(x) ∞ Lp(R) and the following inequality holds with absolute constant c(p) ∈ (0,∞). We find criteria for correct solvability of the problem (0.1) in Lp(R). |