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.
Second order linear difference equations and Karamata sequences / S. Matucci; P. Rehak. - In: INTERNATIONAL JOURNAL OF DIFFERENCE EQUATIONS. - ISSN 0973-6069. - STAMPA. - 3 (2):(2008), pp. 277-288.
Second order linear difference equations and Karamata sequences
MATUCCI, SERENA;
2008
Abstract
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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