| 张伟年.投影下的Gronwall不等式[J].数学研究及应用,1997,17(2):257~260 |
| 投影下的Gronwall不等式 |
| Gronwall Inequality for Projected Systems |
| |
| DOI：10.3770/j.issn:1000-341X.1997.02.023 |
| 中文关键词: 微分方程 Gronwal不等式 有界解 |
| 英文关键词:differential equation Gronwall inequality bounded solution. |
| 基金项目: |
|
| 摘要点击次数: 2911 |
| 全文下载次数: 2105 |
| 中文摘要: |
| 本文对Ｊ．Ｋ．Ｈａｌｅ曾提出的一类广泛的投影下的Ｇｒｏｎｗａｌ不等式问题作了讨论，对满足ｕ（ｔ）≤ａ（ｔ）＋∫０tｂ（ｔ－ｓ）ｕ（ｓ）ｄｓ＋∫０∞ｃ（ｓ）ｕ（ｔ＋ｓ）ｄｓ，(?)ｔ≥０的函数ｕ（ｔ）∈Ｃb0（Ｒ+，Ｒ+）作了估计．其结果对讨论微分方程的有界解、不变流形及其Ｆｏｌｉａｔｉｏｎ和进一步讨论奇性Ｇｒｏｎｗａｌ不等式都有意义 |
| 英文摘要: |
| In this paper we discuss a problem about Gronwall inequality for projected systems, which was mentioned in Hale′s book. An estimate for nonnegative bounded continuous function ｕ（ｔ）≤ａ（ｔ）＋∫０tｂ（ｔ－ｓ）ｕ（ｓ）ｄｓ＋∫０∞ｃ（ｓ）ｕ（ｔ＋ｓ）ｄｓ，(?)ｔ≥０ is given. The conclusion is useful for investigating bounded solutions, invariant manifolds and its foliations for differential equations, and for further discussion on Gronwall inequality with singularity. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
