Regularly varying solutions of second-order difference equations with arbitrary sign coefficient.

Matucci, Serena; Řehák, Pavel

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Asymptotic behavior of solutions to half-linear $q$ -difference equations.

Řehák, Pavel (2011)

Abstract and Applied Analysis

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Second order linear $q$ -difference equations: nonoscillation and asymptotics

Pavel Řehák (2011)

Czechoslovak Mathematical Journal

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The paper can be understood as a completion of the $q$ -Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear $q$ -difference equations. The $q$ -Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice $q^{ℕ_{0}} : = {q^{k} : k \in ℕ_{0}}$ with $q > 1$ . In addition to recalling the existing concepts of $q$ -regular variation and $q$ -rapid variation we introduce $q$ -regularly bounded functions and prove many related properties. The $q$ -Karamata theory...