We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear -difference equation , with , with , to behave like -regularly varying or -rapidly varying or -regularly bounded functions (that is, the functions , for which a special limit behavior of as is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.
Pavel Řehák. "Asymptotic Behavior of Solutions to Half-Linear -Difference Equations." Abstr. Appl. Anal. 2011 (SI1) 1 - 12, 2011. https://doi.org/10.1155/2011/986343