## Abstract

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.

Original language | English |
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Pages (from-to) | 483-508 |

Number of pages | 26 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 146 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jun 2016 |

### Bibliographical note

Publisher Copyright:© 2016 Royal Society of Edinburgh.

## Keywords

- Sturm-Liouville operator
- compactness of resolvent
- estimates of minimal eigenvalues

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