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Detection of positive roots of a polynomial with five parameters

Institution:	1. Department of Mathematics, Tsing Hua University, Hsinchu 30043 Taiwan, ROC;2. Department of Mathematics, Fujian Normal University, Fuzhou, Fujian 350007, People''s Republic of China

Abstract:	We give a complete set of discriminatory criteria for a polynomial with five parameters to have a positive root. This polynomial arises from the characteristic equation of a difference equation Δⁿ(x_k+px_k−τ)+qx_k−σ=0, which is used to model population dynamics. Our investigations are self-contained and based on the theory of envelopes.

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