The Greenspan bound for the order of differential systems
The Greenspan bound for the order of differential systems
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DOI：
10.1090/s0002-9939-1980-0572294-0
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发表时间：
1980-04
期刊：
影响因子：
--
通讯作者：
R. Cohn
中科院分区：
文献类型：
--
作者：
R. Cohn
ABSTRmAC。设S是不定式Y1，…中的一组常微分多项式。。。J·F·Ritt证明了如果M是S的导数维为0的分支，则DX的阶至多为R~(1+)。。。+rn.B.格林斯潘在S的每一个分量都有微分维0的情况下改进了这个界。(他的工作是针对差分方程组进行的，但很容易转移到微分方程组的情况。)结果表明，在没有这一限制的情况下，格林斯潘界限是有效的。
ABsTRmAC. Let S be a system of ordinary differential polynomials in indeterminates Y1, . . . ,yn and of order at most r, iny,, 1 < i < n. It was shown by J. F. Ritt that if M is a component of S of differential dimension 0, then the order of DX is at most r1 + . .. + rn. B. Greenspan improved this bound in the case that every component of S has differential dimension 0. (His work was carried out for difference equations, but is easily transferred to the differential case.) It is shown that the Greenspan bound is valid without this restriction.