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  • 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.
  • 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. (en)
Title
  • On certain asymptotic class of solutions to second order linear q-difference equations
  • On certain asymptotic class of solutions to second order linear q-difference equations (en)
skos:prefLabel
  • On certain asymptotic class of solutions to second order linear q-difference equations
  • On certain asymptotic class of solutions to second order linear q-difference equations (en)
skos:notation
  • RIV/00216224:14410/12:00057291!RIV13-GA0-14410___
http://linked.open...avai/riv/aktivita
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  • P(GAP201/10/1032), Z(AV0Z10190503)
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  • 5
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  • 156188
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  • RIV/00216224:14410/12:00057291
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  • q-difference equation; asymptotic behavior; regular variation; oscillation (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [DD2C0728896B]
http://linked.open...i/riv/nazevZdroje
  • Journal of Physics A: Mathematical and Theoretical
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  • 45
http://linked.open...iv/tvurceVysledku
  • Řehák, Pavel
http://linked.open...ain/vavai/riv/wos
  • 000300259500007
http://linked.open...n/vavai/riv/zamer
issn
  • 1751-8113
number of pages
http://bibframe.org/vocab/doi
  • 10.1088/1751-8113/45/5/055202
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  • 14410
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