### 摘要

In this paper, we study the perturbed abstract Cauchy equation du(t) dt = (A + B)u(t) with initial condition u(0) = x, where A is a generator of a C-semigroup on a Banach space X and B is a relatively bounded linear operator on X. We show that if the perturbation operator B is an A-bounded linear operator which commutates with C and its Abound is sufficiently small, then (A + B) generates a C-semigroup {V(t)}_{t≥0} on X, and hence the perturbed abstract Cauchy problem has a unique mild solution as long as the initial data x is in the subspace [Im(C)]. It is remarkable that we can directly apply these results to some differential equations.

原文 | 英語 |
---|---|

頁（從 - 到） | 555-575 |

頁數 | 21 |

期刊 | Far East Journal of Mathematical Sciences |

卷 | 29 |

發行號 | 3 |

出版狀態 | 已發佈 - 2008 六月 1 |

### ASJC Scopus subject areas

- Mathematics(all)

## 指紋 深入研究「Relative bounded perturbation of abstract cauchy problem」主題。共同形成了獨特的指紋。

## 引用此

Chang, Y. H., & Hong, C. H. (2008). Relative bounded perturbation of abstract cauchy problem.

*Far East Journal of Mathematical Sciences*,*29*(3), 555-575.