Nonexistence of eventually positive solutions of a difference inequality with multiple and variable delays and coefficients

In this paper, we consider the nonexistence of eventually positive solution s of the difference inequality [GRAPHICS] Let m be a positive integer. Then for each positive integer i: 1 less than or equal to i less than or equal to m, {K-i(n)}(n=0)(infinity) and {p(i)(n) }(n=0)(infinity) are a sequence of positive integers and a sequence of nonn egative real numbers, respectively. A sufficient condition guaranteeing the nonexistence of eventually positive solutions is obtained with the help of a new method. As an application of the main result, a conjecture is proved . (C) 2000 Elsevier Science Ltd. All rights reserved.