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

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概要

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• This paper gives several theorems on solution curves of a class of nonlinear equations consisting of <I>n</I> variables and (<I>n</I>-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.

著者

• TAKAHASHI Norikazu

  Kyushu University

関連論文

• Some properties of solution curves of a class of nonlinear equations and the number of solutions
• Some properties of extremal points of solution curves for a class of nonlinear equations
• Proof of an inequality related to the Omega-matrix

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