## Abstract

We consider the equation (Formula presented.) where f ∈ L_{p}(ℝ), p ∈ (1,∞) and (Formula presented). In an earlier paper, we obtained a criterion for correct solvability of (*) in L_{p}(ℝ), p ∈ (1,∞). In this criterion, we use values of some auxiliary implicit functions in the coefficients r and q of equation (*). Unfortunately, it is usually impossible to compute values of these functions. In the present paper we obtain sharp by order, two-sided estimates (an estimate of a function f(x) for x ∈ (a, b) through a function g(x) is sharp by order if c^{−1}|g(x)| ⩽ |f(x)| ⩽ c|g(x)|, x ∈ (a, b), c = const) of auxiliary functions, which guarantee efficient study of the problem of correct solvability of (*) in L_{p}(ℝ), p ∈ (1,∞).

Original language | English |
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Pages (from-to) | 1067-1098 |

Number of pages | 32 |

Journal | Czechoslovak Mathematical Journal |

Volume | 64 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2014 |

### Bibliographical note

Publisher Copyright:© 2014, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.

## Keywords

- Sturm-Liouville equation
- correct solvability

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