Stability in nonlinear neutral differential equations with infinite delay
In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the nonlinear neutral differential equation with infinite delay d/dt x(t) = -a(t) x (t - T1(t)) + d/dt Q (t, x (t - T2(t))) + ∫ D(t,s) f (x (s))ds. An asymptotic stability theorem with a necessary and suff...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Kragujevac, Faculty of Technical Sciences Čačak
2014-01-01
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| Series: | Mathematica Moravica |
| Subjects: | |
| Online Access: | http://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2014/1450-59321402091A.pdf |
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| Summary: | In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the nonlinear neutral differential equation with infinite delay d/dt x(t) = -a(t) x (t - T1(t)) + d/dt Q (t, x (t - T2(t))) + ∫ D(t,s) f (x (s))ds. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton [6], Zhang [17], Althubiti, Makhzoum, Raffoul [1]. |
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| ISSN: | 1450-5932 2560-5542 |