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  • We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear $q$-difference equation $D_q(\Phi(D_q y(t)))+p(t)\Phi(y(qt))=0$, $t\in\{q^k:k\in\N_0\}$ with $q>1$, $\Phi(u)=|u|^{\alpha-1}\sgn u$ with $\alpha>1$, to behave like $q$-regularly varying or $q$-rapidly varying or $q$-regularly bounded functions (i.e., the functions $y$, for which a special limit behavior of $y(qt)/y(t)$ as $t\to\infty$ is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.
  • We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear $q$-difference equation $D_q(\Phi(D_q y(t)))+p(t)\Phi(y(qt))=0$, $t\in\{q^k:k\in\N_0\}$ with $q>1$, $\Phi(u)=|u|^{\alpha-1}\sgn u$ with $\alpha>1$, to behave like $q$-regularly varying or $q$-rapidly varying or $q$-regularly bounded functions (i.e., the functions $y$, for which a special limit behavior of $y(qt)/y(t)$ as $t\to\infty$ is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented. (en)
Title
  • Asymptotic behavior of solutions to half-linear q-difference equations
  • Asymptotic behavior of solutions to half-linear q-difference equations (en)
skos:prefLabel
  • Asymptotic behavior of solutions to half-linear q-difference equations
  • Asymptotic behavior of solutions to half-linear q-difference equations (en)
skos:notation
  • RIV/00216224:14410/11:00050561!RIV12-GA0-14410___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GAP201/10/1032), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika
  • 986343
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 187373
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14410/11:00050561
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • regular variation; q-difference equation; asymptotic behavior; oscillation (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [E112022FA426]
http://linked.open...i/riv/nazevZdroje
  • Abstract and Applied Analysis
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2011
http://linked.open...iv/tvurceVysledku
  • Řehák, Pavel
http://linked.open...n/vavai/riv/zamer
issn
  • 1085-3375
number of pages
http://localhost/t...ganizacniJednotka
  • 14410
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