Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument
Consider the first-order delay difference equation with a constant argument Δxn+pnxn-k=0, n=0,1,2,…, and the delay difference equation with a variable argument Δxn+pnxτn=0, n=0,1,2,…, where p(n) is a sequence of nonnegative real numbers, k is a positive integer, Δx(n)=x(n+1)-x(n), and τ(n) is a se...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/9416319 |
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| Summary: | Consider the first-order delay difference equation with a constant argument Δxn+pnxn-k=0, n=0,1,2,…, and the delay difference equation with a variable argument Δxn+pnxτn=0, n=0,1,2,…, where p(n) is a sequence of nonnegative real numbers, k is a positive integer, Δx(n)=x(n+1)-x(n), and τ(n) is a sequence of integers such that τ(n)≤n-1 for all n≥0 and limn→∞τ(n)=∞. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given. |
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| ISSN: | 1026-0226 1607-887X |