On the difference equation \(x_{n+1}=\frac{a+\alpha x_n+\alpha x_{n-1}+\cdots+\alpha x_{n-k+2}}{x_{n-k+1}}\) (Q1405083)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the difference equation \(x_{n+1}=\frac{a+\alpha x_n+\alpha x_{n-1}+\cdots+\alpha x_{n-k+2}}{x_{n-k+1}}\) |
scientific article; zbMATH DE number 1970659
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the difference equation \(x_{n+1}=\frac{a+\alpha x_n+\alpha x_{n-1}+\cdots+\alpha x_{n-k+2}}{x_{n-k+1}}\) |
scientific article; zbMATH DE number 1970659 |
Statements
On the difference equation \(x_{n+1}=\frac{a+\alpha x_n+\alpha x_{n-1}+\cdots+\alpha x_{n-k+2}}{x_{n-k+1}}\) (English)
0 references
25 August 2003
0 references
Some theorems are proved showing that the solutions of \[ x_{n+1}= {a+ \alpha x_n+\alpha x_{n-1}+\cdots +\alpha x_{n-k+2}\over x_{n-k+1}},\;n=k-1,k,\dots \] are strictly oscillatory and bounded.
0 references
difference equations
0 references
oscillatory solutions
0 references
persistence
0 references
bounded solutions
0 references
0.9866222
0 references
0.9836844
0 references
0.98143137
0 references
0.9778186
0 references
0.9756256
0 references
0.9697629
0 references
0.96881884
0 references
