Fixed points and stability in nonlinear neutral integro-differential equations with variable delay
Keyword(s):
The nonlinear neutral integro-differential equation x'(t) = -?t,t-?(t) a (t,s) g(x(s))ds+c(t)x'(t-?(t)), with variable delay ?(t) ? 0 is investigated. We find suitable conditions for ?, a, c and g so that for a given continuous initial function ? mapping P for the above equation can be defined on a carefully chosen complete metric space S0? in which P possesses a unique fixed point. The final result is an asymptotic stability theorem for the zero solution with a necessary and sufficient conditions. The obtained theorem improves and generalizes previous results due to Burton [6], Becker and Burton [5] and Jin and Luo [16].
2006 ◽
Vol 136
(2)
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pp. 245-275
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1994 ◽
Vol 17
(4)
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pp. 713-716
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2018 ◽
Vol 56
(2)
◽
pp. 3-12
Keyword(s):