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

0458376 - MÚ 2017 RIV GB eng J - Článek v odborném periodiku
Řehák, Pavel
Asymptotic formulae for solutions of linear second--order difference equations.
Journal of Difference Equations and Applications. Roč. 22, č. 1 (2016), s. 107-139. ISSN 1023-6198. E-ISSN 1563-5120
Institucionální podpora: RVO:67985840
Klíčová slova: linear difference equation * asymptotic behavior * nonoscillatory solution
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.762, rok: 2016
http://www.tandfonline.com/doi/abs/10.1080/10236198.2015.1077815?journalCode=gdea20

We study asymptotic behavior of solutions to the (nonoscillatory) linear difference equation $Delta(r_kDelta y_k)=p_k y_{k+1},$ where $p,r$ are positive sequences defined on ${m,m+1,m+2,dots}subsetZ$. 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.
Trvalý link: http://hdl.handle.net/11104/0258640