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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| Format: | Article |
| Language: | English |
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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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| author | G. M. Moremedi I. P. Stavroulakis |
| author_facet | G. M. Moremedi I. P. Stavroulakis |
| author_sort | G. M. Moremedi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d536c48d340442cabb0ba304f3b82e4e |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d536c48d340442cabb0ba304f3b82e4e2025-08-20T03:19:42ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/94163199416319Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone ArgumentG. M. Moremedi0I. P. Stavroulakis1Department of Mathematical Sciences, University of South Africa, Pretoria 0003, South AfricaDepartment of Mathematical Sciences, University of South Africa, Pretoria 0003, South AfricaConsider 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.http://dx.doi.org/10.1155/2018/9416319 |
| spellingShingle | G. M. Moremedi I. P. Stavroulakis Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument Discrete Dynamics in Nature and Society |
| title | Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument |
| title_full | Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument |
| title_fullStr | Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument |
| title_full_unstemmed | Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument |
| title_short | Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument |
| title_sort | oscillation conditions for difference equations with a monotone or nonmonotone argument |
| url | http://dx.doi.org/10.1155/2018/9416319 |
| work_keys_str_mv | AT gmmoremedi oscillationconditionsfordifferenceequationswithamonotoneornonmonotoneargument AT ipstavroulakis oscillationconditionsfordifferenceequationswithamonotoneornonmonotoneargument |