Asymptotic formulas for q-regularly varying solutions of half-linear q-difference equations
| dc.contributor.author | Djordjevic, Katarina | |
| dc.date.accessioned | 2021-08-27T14:02:03Z | |
| dc.date.available | 2021-08-27T14:02:03Z | |
| dc.date.issued | 2021-06-08 | |
| dc.description.abstract | This article studies the asymptotic behavior of positive solutions of the q-difference half-linear equation Dq(p(t)Φ(Dq(x(t)))) + r(t)Φ(x(qt)) = 0, t ∈ qℕ0 := {qn : n ∈ ℕ0}, where q > 1, Φ(x) = |x|α sgn x, α > 0, p : qℕ0 → (0, ∞), r : qℕ0 → ℝ, in the framework of q-regular variation. In particular, if r is eventually of one sign, p and |r| are q-regularly varying functions such that tα+1 r(t)/p(t) → 0, as t → ∞, we obtain asymptotic formulas for the q-regularly varying solutions. Moreover, when p(t) ≡ 1 and r is an eventually positive or eventually negative function, we obtain an asymptotic formula of a q-slowly varying solution. Using generalized regularly varying sequences, we apply these results to the half-linear difference equation case. At the end, we illustrate the obtained results with examples. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 23 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Djordjević, K. S. (2021). Asymptotic formulas for q-regularly varying solutions of half-linear q-difference equations. <i>Electronic Journal of Differential Equations, 2021</i>(50), pp. 1-23. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14460 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | q-difference equation | |
| dc.subject | non-oscillatory solution | |
| dc.subject | asymptotic behavior | |
| dc.subject | regular variation | |
| dc.subject | q-regular variation | |
| dc.subject | half-linear equation | |
| dc.title | Asymptotic formulas for q-regularly varying solutions of half-linear q-difference equations | |
| dc.type | Article |