Rapidly varying decreasing solutions of half-linear difference equations

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Authors

MATUCCI Serena ŘEHÁK Pavel

Year of publication 2009
Type Article in Periodical
Magazine / Source Mathematical and Computer Modelling
MU Faculty or unit

Faculty of Education

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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