Second Order Linear Difference Equations and Karamata Sequences
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Difference Equations |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Regularly varying sequence; rapidly varying sequence; linear difference equation; nonoscillatory solution |
| Description | We establish necessary and sufficient conditions for all positive solutions of a linear second order difference equation to be Karamata sequences, i.e., slowly varying or regularly varying or rapidly varying. Moreover, we discuss relations with the standard classification of nonoscillatory solutions and with the notion of recessive solutions. Our results lead to a complete characterization of positive solutions with respect to their regularly or rapidly varying behavior. |
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