Liouvillian solutions of first order nonlinear differential equations

被引：7
|
作者：
Srinivasan, Varadharaj Ravi [1 ]
机构：
[1] IISER Mohali, Dept Math Sci, Sas Nagar 140306, Punjab, India
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2017年 / 221卷 / 02期
关键词：
D O I：
10.1016/j.jpaa.2016.07.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let k be a differential field of characteristic zero and E be a liouvillian extension of k. For any differential subfield K intermediate to E and k, we prove that there is an element in the set K - k satisfying a linear homogeneous differential equation over k. We apply our results to study liouvillian solutions of first order nonlinear differential equations and provide generalisations and new proofs for several results of M. Singer and M. Rosenlicht on this topic. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：411 / 421
页数：11
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