## Abstract

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_{1}^{loc}(R). By a solution of equation (1), we mean any function y(x) such that y(x), y′(x) ∈ 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 L_{p}(R), p ∈ [1, ∞].

Original language | English |
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Pages (from-to) | 1043-1054 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 130 |

Issue number | 4 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |

## Keywords

- Correct solvability
- Sturm-Liouville equation

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