## Abstract

We consider the equation -(r(x)y′(x))′+q(x)y(x)=f(x),x∈Rwhere f∈ L_{1}(R) and r>0,q≥0,1/r∈L1loc(R),q∈L1loc(R),lim|d|→∞∫x-dxdtr(t)·∫x-dxq(t)dt=∞.By a solution of (1), we mean any function y, absolutely continuous in R together with ry^{′}, which satisfies (1) almost everywhere in R. Under conditions (2) and (3), we give a criterion for correct solvability of (1) in the space L_{1}(R).

Original language | English |
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Pages (from-to) | 417-443 |

Number of pages | 27 |

Journal | Bolletino dell Unione Matematica Italiana |

Volume | 11 |

Issue number | 4 |

DOIs | |

State | Published - 1 Dec 2018 |

## ASJC Scopus subject areas

- Mathematics (all)

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