q-regular variation and q-difference equations
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | J. Phys. A: Math. Gen. |
| MU Faculty or unit | |
| 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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