The class of second order nonlinear neutral integro-differential equations x(t)+f(t,x(t),x(t))x(t)+∑_{j=1}^{N}∫_{t-τ_{j}(t)}^{t}a_{j}(t,s)g_{j}(s,x(s))ds +∑_{j=1}^{N}b_{j}(t)x′(t-τ_{j}(t))=0.with variable delays τ_{j}(t)≥0, 0≤j≤N, is investigated, where t-τ_{j}(t) is supposed to be strictly increasing. We give new conditions ensuring that the zero solution is asymptotically stable by means of the fixed point theory. Our work extends and improves previous results in the literature such as, D. Pi <cite>pi1</cite> and T.A. Burton <cite>b12</cite>. An example is given to illustrate our claim.
@article{4574,
title = {Nonlinear neutral integro-differential equations, stability by fixed point and inverses of delays},
journal = {Novi Sad Journal of Mathematics},
volume = {46},
year = {2017},
language = {EN},
url = {http://dml.mathdoc.fr/item/4574}
}
Gabsi, Hocine; Ardjouni, Abdelouaheb; Djoudi, Ahcene. Nonlinear neutral integro-differential equations, stability by fixed point and inverses of delays. Novi Sad Journal of Mathematics, Tome 46 (2017) . http://gdmltest.u-ga.fr/item/4574/