Consider the retarded difference equation x<sub>n</sub>-x<sub>n-1</sub>=F（-f（x<sub>n</sub>）+g（x<sub>n</sub>-k））, （*） where k is a positive integer, F,f,g:R→R a...Consider the retarded difference equation x<sub>n</sub>-x<sub>n-1</sub>=F（-f（x<sub>n</sub>）+g（x<sub>n</sub>-k））, （*） where k is a positive integer, F,f,g:R→R are continuous, F and f are increasing on R, and uF（u）】0 for all u≠0. We show that when f（y）≥g（y）（resp. f（y）≤g（y）） for y∈R, every solution of （*） tends to either a constant or -∞ （resp. ∞） as n→∞. Furthermore, if f（y）≡g（y） for y∈R, then every solution of （*） tends to a constant as n→∞.展开更多
基金Project supported by NNSF (19601016) of China NSF (97-37-42) of Hunan
文摘Consider the retarded difference equation x<sub>n</sub>-x<sub>n-1</sub>=F（-f（x<sub>n</sub>）+g（x<sub>n</sub>-k））, （*） where k is a positive integer, F,f,g:R→R are continuous, F and f are increasing on R, and uF（u）】0 for all u≠0. We show that when f（y）≥g（y）（resp. f（y）≤g（y）） for y∈R, every solution of （*） tends to either a constant or -∞ （resp. ∞） as n→∞. Furthermore, if f（y）≡g（y） for y∈R, then every solution of （*） tends to a constant as n→∞.
