On certain asymptotic class of solutions to second order linear q-difference equations
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Physics A: Mathematical and Theoretical |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1088/1751-8113/45/5/055202 |
| Field | General mathematics |
| Keywords | q-difference equation; asymptotic behavior; regular variation; oscillation |
| Description | 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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