ON AN INFINITE SET OF NON-LINEAR DIFFERENTIAL EQUATIONS
ON AN INFINITE SET OF NON-LINEAR DIFFERENTIAL EQUATIONS
复制标题
关于无限组非线性微分方程
DOI：
10.1093/qmath/13.1.119
复制
发表时间：
1962
影响因子：
0.7
通讯作者：
J. McLeod
中科院分区：
文献类型：
--
作者：
J. McLeod
我们关心的是自变量t的正值，它是物理上的时间，常数aif是正的和对称的，即ati ^ 0，a^ = ait。从纯数学观点看，对这类问题所做的唯一工作，实际上仅限于ow有界的情况，如（1）、（2）。把a y推广到无界似乎很困难，但本文首先明确地解决了一个特殊的情况，当ati = ij时，并在§ 4中证明了在相当一般的条件下关于atj的存在性定理（尽管不是唯一性定理）。我希望在以后的论文中再回到唯一性问题和其他相关问题。
We are concerned with positive values of the independent variable t, which is physically the time, and the constant coefficients aif are positive and symmetric, i.e. ati ^ 0, a^ = ait. The only work that seems to have been done on this type of problem from the pure-mathematical point of view has been restricted, in effect, to the case where ow is bounded, as in (1), (2). The extension to unbounded a y appears difficult, but this paper makes a start on the problem by solving explicitly one specific case, when ati = ij, and by proving, in § 4, an existence theorem (though not a uniqueness theorem) under fairly general conditions on atj. I hope to return to the problem of uniqueness and other related questions in a later paper.