q-regular variation and q-difference equations

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Authors

ŘEHÁK Pavel VÍTOVEC Jiří

Year of publication 2008
Type Article in Periodical
Magazine / Source J. Phys. A: Math. Gen.
MU Faculty or unit

Faculty of Education

Citation
Doi http://dx.doi.org/10.1088/1751-8113/41/49/495203
Field General mathematics
Keywords q-calculus; regularly varying function; q-difference equation; asymptotic behavior
Description We introduce the concept of $q$-regularly varying functions and establish basic properties of such functions. Among others it is shown that considering regular variation in $q$-calculus is somehow natural and leads to interesting observations and simplifications comparing with classical continuous and discrete theories. The obtained theory is applied to an investigation of asymptotic behavior of solutions to linear second order $q$-difference equations.
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