Asymptotic behavior of linear advanced dynamic equations on time scales.

Resumen

Let T be a time scale which is unbounded above and below and such that t0∈ T. Let id + h, id + r: [t0,∞) ∩ T → T  be such that (id + h)([t0,∞) ∩ T) and (id + r)([t0,∞) ∩ T) are time scales. We use the contraction mapping theorem to obtain convergence to zero about the solution for the following linear advanced dynamic equation  x△ (t) + a (t) xσ (t + h (t)) + b (t) xσ (t + r (t)) = 0, t ∈ [t0, ∞) ∩ T   where f△ is the △-derivative on T. 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.

Biografía del autor

Malik Belaid, University of Annaba.
Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics.
Abdelouaheb Ardjouni, University of Souk Ahras.
Department of Mathematics and Informatics .
Ahcene Djoudi, University of Annaba.
Department of Mathematics, Applied Mathematics Lab, Faculty of Sciences.

Citas

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Publicado
2019-02-26
Cómo citar
Belaid, M., Ardjouni, A., & Djoudi, A. (2019). Asymptotic behavior of linear advanced dynamic equations on time scales. Proyecciones. Revista De Matemática, 38(1), 97-110. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2379
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