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Rapidly varying decreasing solutions of half-linear difference equations

✍ Scribed by Serena Matucci; Pavel Řehák

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
471 KB
Volume
49
Category
Article
ISSN
0895-7177

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✦ Synopsis

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 -∞. 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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