On the stability of equilibrium for almost periodic systems

Ignatyev, Alexander O.

doi:10.1016/s0362-546x(96)00078-8

Cited by 15 publications

(5 citation statements)

References 4 publications

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“…Note that Barbašin and Krasovskiȋ's theorem cannot be extended to a general case of nonautonomous systems (refer to [44]). Much ink has been spent on extensions of the Barbašin-Krasovskiȋ-LaSalle method (for example, see [4,9,18,19,23,29,30,38,55]). …”

Section: Theorem 32 Let Assumptions ( a 1 ) And (A 2 ) Hold And Suppmentioning

confidence: 99%

Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients

Sugie

Hata

2011

Monatsh Math

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The following system considered in this paper:This system is referred to as a half-linear system. The coefficient f (t) is assumed to be bounded, but the coefficients e(t), g(t) and h(t) are not necessarily bounded. Sufficient conditions are obtained for global asymptotic stability of the zero solution.Our results can be applied to not only the case that the signs of f (t) and g(t) change like the periodic function but also the case that f (t) and g(t) irregularly have zeros.Some suitable examples are included to illustrate our results.

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Section: Theorem 32 Let Assumptions ( a 1 ) And (A 2 ) Hold And Suppmentioning

confidence: 99%

Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients

Sugie

Hata

2011

Monatsh Math

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“…In this case Barbashin and Krasovskii proved a well-known result [2] on asymptotic stability. This result was extended in [9], [10] and [11] to the case of periodic and almost periodic systems.…”

Section: Introductionmentioning

confidence: 90%

Barbashin-Krasovskii theorem for stochastic differential equations

Ignatyev

Mandrekar

2010

Proc. Amer. Math. Soc.

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“…Именно для таких систем Барбашиным и Красовским [2] получен эффективный критерий асимптотической устойчивости для случая авто-номных систем обыкновенных дифференциальных уравнений. В дальнейшем, ис-пользуя эту идею, аналогичные теоремы были доказаны для периодических и почти периодических систем обыкновенных дифференциальных уравнений [3]- [6], для сис-тем функционально-дифференциальных уравнений с запаздыванием [7]- [13] для стохастических дифференциальных уравнений [14], для дифференциальных вклю-чений [15], для дифференциальных уравнений в банаховом пространстве [16] и для исследования устойчивости относительно части переменных [17]. Отметим также работы [18]- [24], в которых для исследования устойчивости применяются знакопо-стоянные функции (функционалы) Ляпунова.…”

Section: Doi: 104213/mzm9078unclassified