Title | SMITH-TYPE STABILITY THEOREMS FOR THE DAMPED LINEAR OSCILLATOR |

Publication Type | Journal Article |

Year of Publication | 2018 |

Authors | HATVANI L. |

Journal | Dynamic Systems and Applications |

Volume | 27 |

Issue | 2 |

Start Page | 299 |

Pagination | 20 |

Date Published | 03/2018 |

ISSN | 1056-2176 |

AMS Subject Classification | 34D20, 70J25 |

Abstract | Sufficient conditions are given guaranteeing that every solution of the equation \[x''+h(t)x'+\omega^2x=0 \qquad (h(t)\ge 0,\ x\in {\mathbb{R}})\] and its derivative tend to zero as $t\to\infty$. The results are applicable in the general case $0\le 0\le h(t)<\infty$, i.e., conditions $h(t)\ge$const.$>0$ and $h(t)\le$const.$<\infty$ are not required in general. In the first main theorem the damping is controlled on the whole half-line $[0,\infty)$. The second main theorem is devoted to the problem of the intermittent damping, when conditions are supposed only on the union of non-overlapping intervals. |

https://acadsol.eu/dsa/articles/27/2/6.pdf | |

DOI | 10.12732/dsa.v27i2.6 |

Refereed Designation | Refereed |