On certain asymptotic class of solutions to second order linear q-difference equations
| Autoři | |
|---|---|
| Rok publikování | 2012 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Journal of Physics A: Mathematical and Theoretical |
| Fakulta / Pracoviště MU | |
| Citace | |
| Doi | http://dx.doi.org/10.1088/1751-8113/45/5/055202 |
| Obor | Obecná matematika |
| Klíčová slova | q-difference equation; asymptotic behavior; regular variation; oscillation |
| Popis | The paper deals with the linear second order $q$-difference equation $y(q^2t)+a(t)y(qt)+b(t)y(t)=0$, $b(t)\ne 0$, considered on $\{q^k:k\in\N_0\}$, $q>1$. The class of functions satisfying the relation $y(qt)/y(t)\sim\omega(t)$ as $t\to\infty$ for some function $\omega$ is introduced and studied. Sufficient and necessary conditions are established for the equation to have solutions in this class. Related results concerning estimates for solutions and (non)oscillation of all solutions are discussed. A comparison with existing results is made and some applications are given. |
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