In this paper we use the contraction mapping theorem to obtain asymptotic stability results about the zero solution for the following mixed linear delay Levin-Nohel integro-dynamic equation x^{Δ}(t)+∫_{t-r(t)}^{t}a(t,s)x(s)Δs+b(t)x(t-h(t))=0, t∈[t₀,∞)∩T,where f^{△} is the △-derivative on T. An asymptotic stability theorem with a necessary and sufficient condition is proved. The results obtained here extend the work of Dung <cite>d</cite>. In addition, the case of the equation with several delays is studied.
@article{37758,
title = {Stability in mixed linear delay Levin-Nohel integro-dynamic equations on time scales},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {38},
year = {2019},
doi = {10.5269/bspm.v38i5.37758},
language = {EN},
url = {http://dml.mathdoc.fr/item/37758}
}
Ali Khelil, Kamel; Ardjouni, Abdelouaheb; Djoudi, Ahcene. Stability in mixed linear delay Levin-Nohel integro-dynamic equations on time scales. Boletim da Sociedade Paranaense de Matemática, Tome 38 (2019) . doi : 10.5269/bspm.v38i5.37758. http://gdmltest.u-ga.fr/item/37758/