Informace o publikaci

Asymptotic formulae for solutions of linear second--order difference equations

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ŘEHÁK Pavel

Druh Článek v odborném periodiku
Časopis / Zdroj J. Difference Equ. Appl.
Fakulta / Pracoviště MU

Pedagogická fakulta

Citace
www http://dx.doi.org/10.1080/10236198.2015.1077815
Doi http://dx.doi.org/10.1080/10236198.2015.1077815
Obor Obecná matematika
Klíčová slova linear difference equation; asymptotic behavior; nonoscillatory solution; regularly varying sequence
Popis We study asymptotic behavior of solutions to the (nonoscillatory) linear difference equation $\Delta(r_k\Delta y_k)=p_k y_{k+1},$ where $p,r$ are positive sequences defined on $\{m,m+1,m+2,\dots\}\subset\Z$. We establish sufficient conditions (in terms of regular variation) for all eventually positive solutions to satisfy certain asymptotic formulae. As a by--product, we obtain regular variation of all these solutions and some other of their properties. Various related problems are discussed and several examples are given.