Authors: | Stević, Stevo |

Title: | Note on some consequences of a problem by Dellac |

Journal: | Advances in Difference Equations |

Volume: | 2019 |

Issue: | 1 |

Issue Date: | 1-Dec-2019 |

Rank: | M21а |

ISSN: | 1687-1847 |

DOI: | 10.1186/s13662-019-2237-7 |

Abstract: | By using a solvability method for differential equations, we present an elegant and straightforward/direct proof of the following slight generalization of a classical result: Let ω> 0 and f be a two times continuously-differentiable function on the closed non-degenerated interval [a, b] such that f(a) = f(b) = 0 , f(x) > 0 , x∈ (a, b) , and f″(x)+ω2f(x)>0,x∈(a,b). Then the following inequality holds b− a> π/ ω, which is strict. For the case when f is continuous on [a, b] and two times differentiable function on (a, b) , such that f(a) = f(b) = 0 , f(x) > 0 , x∈ (a, b) , and (p(x)f′(x))′+f(x)>0,x∈(a,b), where p is a continuous function on [a, b] , differentiable on (a, b) , and such that p(x)≥1ω2for x∈[a,b], for some ω> 0 , we show by using the methods of differential calculus that then it holds b− a≥ π/ ω. |

Keywords: | Estimate of the distance between zeros | Linear differential equation of second order | Solvability method |

Publisher: | Springer Link |

Project: | Modulation of intracellular energy balance-controlling signalling pathways in therapy of cancer and neuro-immuno-endocrine disorders Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education |

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