Stability in Totally Nonlinear Neutral Dynamic Equations on Time Scales

• Main Authors: Malik Belaid, Abdelouaheb Ardjouni, Ahcene Djoudi
• Format: Article
• Language: English
• Published: Etamaths Publishing 2016-06-01
• Series: International Journal of Analysis and Applications
• Online Access: http://etamaths.com/index.php/ijaa/article/view/754

<p>Let T be a time scale which is unbounded above and below and such that 0∈T. Let id-τ:[0,∞)∩T→T be such that (id-τ)([0,∞)∩T) is a time scale. We use the Krasnoselskii-Burton's fixed point theorem to obtain stability results about the zero solution for the following totally nonlinear neutral dynamic equation with variable delay</p> <p>x^{△}(t)=-a(t)h(x^{σ}(t))+c(t)x^{△}(t-τ(t))+b(t)G(x(t),x(t-τ(t))), t∈[0,∞)∩T,</p> where f^{△} is the △-derivative on T and f^{△} is the △-derivative on (id-τ)(T). The results obtained here extend the work of Ardjouni, Derrardjia and Djoudi [2].