Research ArticleNo Access

Systems of polynomials with at least one positive real zero

School of Mathematical Sciences, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing, 100871, China

E-mail Address: wangjie212@mails.ucas.ac.cn

https://doi.org/10.1142/S0219498820501832Cited by:1 (Source: Crossref)

Abstract

In this paper, we prove several theorems on systems of polynomials with at least one positive real zero based on the theory of conceive polynomials. These theorems provide sufficient conditions for systems of multivariate polynomials admitting at least one positive real zero in terms of their Newton polytopes and combinatorial structure. Moreover, a class of polynomials attaining their global minimums in the first quadrant are given, which is useful in polynomial optimization.

Communicated by J. Hauenstein

Keywords:

AMSC: 12D10, 13J30, 14P10, 90C30

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