多滞量差分不等式最终正解的不存在性

Non-existence of eventually positive solution of difference inequality with several delay quantities

考虑到以下形式的差分不等式的最终正解的不存在性 ,yn+1-yn+ ∑mi=1pi(n)yn-ki ≤ 0 ( ) ,其中m≥ 1,pi(n)≥ 0。证明了如果对一切λ∈ (0 ,1)limn→∞inf∑mi=1pi(n) [λ(1-λ) ki]- 1>1( ) ,则 ( )

This paper concerns with non-existence of eventually positive solutions of defference inequality of the form y n+1-y n+∑mi=1p i(n)y n-k i≤0(*),where m≥1,p i(n)≥0。It is proved that for any λ∈(0,1),if limn→∞inf∑mi=1p i(n)[λ(1-λ) k i] -1>1(**),then inequality (*)does not have any eventually positive solution.