Rapidly varying decreasing solutions of half-linear difference equations
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Periodical |
| Magazine / Source | Mathematical and Computer Modelling |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.mcm.2008.09.002 |
| Field | General mathematics |
| Keywords | Rapidly varying sequence; regularly varying sequence; half-linear difference equation; nonoscillatory solution. |
| Description | In this paper a necessary and sufficient condition is derived for all positive decreasing solutions of a half-linear second order difference equation to be rapidly varying of index - infinity. Relations with the standard classification of nonoscillatory solutions and with the notion of recessive solutions are also discussed. The results of this paper are complementary to those of a previous paper by the authors, and lead to a complete characterization of positive decreasing solutions with respect to their regularly or rapidly varying behavior. |
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