Informace o publikaci

On certain asymptotic class of solutions to second order linear q-difference equations



Rok publikování 2012
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Physics A: Mathematical and Theoretical
Fakulta / Pracoviště MU

Pedagogická fakulta

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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