Some properties of solution curves of a class of nonlinear equations and the number of solutions

被引：0
|
作者：
Nishi, Tetsuo [1 ]
Oishi, Shin'ichi [1 ,3 ]
Takahashi, Norikazu [2 ]
机构：
[1] Waseda Univ Okubo, Sch Sci & Engn, Shinjuku Ku, Tokyo 1690072, Japan
[2] Kyushu Univ Motooka, Nishi Ku, Fukuoka 8190395, Japan
[3] CREST, JST, Tokyo, Japan
来源：
IEICE NONLINEAR THEORY AND ITS APPLICATIONS | 2012年 / 3卷 / 03期
关键词：
solution curve; rank of Jacobian matrix; O-matrix; number of solutions; system of nonlinear equations; irreducible matrix;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper gives several theorems on solution curves of a class of nonlinear equations consisting of n variables and (n - 1) equations. In particular we give a remarkable theorem on the rank of a Jacobian matrix associated with the above equations. For the proof of these theorems the O-matrix, which one of the authors defined previously, and the irreducible matrix play a definitely important role. As the result we show that the solution curves consist of only two types of curves.
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页码：301 / 335
页数：35
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