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 |
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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. |
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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. |
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