TY - JOUR AU - Belaid, Malik AU - Ardjouni, Abdelouaheb AU - Djoudi, Ahcene PY - 2019/02/26 Y2 - 2024/03/28 TI - Asymptotic behavior of linear advanced dynamic equations on time scales. JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 38 IS - 1 SE - DO - UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/2379 SP - 97-110 AB - <p>Let T be a time scale which is unbounded above and below and such that <em>t<sub>0</sub> </em>∈ <strong>T</strong>. Let <em>id</em>&nbsp;+ <em>h, id</em> + <em>r</em>: [<em>t<sub>0</sub></em>,∞) ∩ <strong>T</strong> → <strong>T</strong>&nbsp; be such that&nbsp;(<em>id</em> + <em>h</em>)([<em>t<sub>0</sub></em>,∞) ∩ <strong>T</strong>) and (<em>id&nbsp;</em>+ <em>r</em>)([<em>t<sub>0</sub></em>,∞) ∩ <strong>T</strong>) are time scales. We use the contraction mapping theorem to obtain convergence to zero about the solution for the following linear advanced dynamic equation</p><table style="width: 100%;" border="0"><tbody><tr><td style="text-align: center;">&nbsp;x<sup>∆</sup> (t) + a (t) x<sup>σ</sup> (t + h (t)) + b (t) x<sup>σ</sup> (t + r (t)) = 0, t ∈ [t<sub>0</sub>, ∞) ∩ <strong>T</strong></td></tr></tbody></table><p>&nbsp;</p><p>where f<sup>∆</sup> is the ∆-derivative on <strong>T</strong>. A convergence theorem with a necessary and sufficient condition is proved. The results obtained here extend the work of Dung [11]. In addition, the case of the equation with several terms is studied.</p> ER -