Stability in Totally Nonlinear Neutral Dynamic Equations on Time Scales

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Malik Belaid, Abdelouaheb Ardjouni, Ahcene Djoudi, Stability in Totally Nonlinear Neutral Dynamic Equations on Time Scales, Int. J. Anal. Appl., 11 (2) (2016), 110-123.

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Malik Belaid, Abdelouaheb Ardjouni, Ahcene Djoudi

Abstract

Let T be a time scale which is unbounded above and below and such that 0∈T. Let id-Ï„:[0,∞)∩T→T be such that (id-Ï„)([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

x^{â–³}(t)=-a(t)h(x^{σ}(t))+c(t)x^{â–³}(t-Ï„(t))+b(t)G(x(t),x(t-Ï„(t))), t∈[0,∞)∩T,

where f^{â–³} is the â–³-derivative on T and f^{â–³} is the â–³-derivative on (id-Ï„)(T). The results obtained here extend the work of Ardjouni, Derrardjia and Djoudi [2].

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