Publication details
Asymptotic formulae for solutions of linear second--order difference equations
| Authors | |
|---|---|
| Year of publication | 2016 |
| Type | Article in Periodical |
| Magazine / Source | J. Difference Equ. Appl. |
| MU Faculty or unit | |
| Citation | |
| web | http://dx.doi.org/10.1080/10236198.2015.1077815 |
| Doi | https://doi.org/10.1080/10236198.2015.1077815 |
| Field | General mathematics |
| Keywords | linear difference equation; asymptotic behavior; nonoscillatory solution; regularly varying sequence |
| Description | We study asymptotic behavior of solutions to the (nonoscillatory) linear difference equation $\Delta(r_k\Delta y_k)=p_k y_{k+1},$ where $p,r$ are positive sequences defined on $\{m,m+1,m+2,\dots\}\subset\Z$. We establish sufficient conditions (in terms of regular variation) for all eventually positive solutions to satisfy certain asymptotic formulae. As a by--product, we obtain regular variation of all these solutions and some other of their properties. Various related problems are discussed and several examples are given. |