Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:B1L-A

Session:

Number:288

A theorem on a solution curve of a class of nonlinear equations

Tetsuo Nishi,  Shin'ichi Oishi,  Norikazu Takahashi,  

pp.288-291

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.288

PDF download (413.8KB)

This paper gives an important theorem on a solution curve of a class of nonlinear equations consisting of n variables and (n - 1) equations, which is obtained from a typical nonlinear equation F(x) +Ax = b by deleting the first equation. The theorem is obtained under the assumption that A is an Ω-matrix, which is a generalization of a P-matrix and a positive definite matrix. From this theorem and the previous results we can derive some very important properties on a solution curve. That is, the solution curves consist of only two types of curves.

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