Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Section on Analysis, Design and Optimization of Nonlinear Circuits
Some properties of solution curves of a class of nonlinear equations and the number of solutions
Tetsuo NishiShin'ichi OishiNorikazu Takahashi
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2012 Volume 3 Issue 3 Pages 301-335


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 Ω-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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© 2012 The Institute of Electronics, Information and Communication Engineers
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