Publication details

Second Order Linear Difference Equations and Karamata Sequences

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Authors

ŘEHÁK Pavel MATUCCI Serena

Year of publication 2008
Type Article in Periodical
Magazine / Source International Journal of Difference Equations
MU Faculty or unit

Faculty of Education

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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