A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n) = -p(n)x(n - k) with a Positive Coefficient

被引：16

作者：

Bastinec, J. ^{[1
]}

Berezansky, L. ^{[2
]}

Diblik, J. ^{[1
,3
]}

Smarda, Z. ^{[1
]}

机构：

[1] Brno Univ Technol, Fac Elect Engn & Commun, Dept Math, Brno 61600, Czech Republic

[2] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

[3] Brno Univ Technol, Fac Civil Engn, Dept Math & Descript Geometry, Brno 60200, Czech Republic

来源：

ABSTRACT AND APPLIED ANALYSIS | 2011年

关键词：

RATIONAL DIFFERENCE EQUATION; NONTRIVIAL SOLUTIONS; CRITICAL-STATE; EXISTENCE; ASYMPTOTICS; CRITERIA;

D O I：

10.1155/2011/586328

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A linear (k + 1)th-order discrete delayed equation Delta x(n) = -p(n)x(n - k) where p(n) a positive sequence is considered for n -> infinity. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for p(n), all solutions of the equation considered are oscillating for n -> infinity.

引用

页数：28