Nonmonotone functionals in the Lyapunov direct method for equations of the neutral type (Q1935403)
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scientific article; zbMATH DE number 6136681
| Language | Label | Description | Also known as |
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| English | Nonmonotone functionals in the Lyapunov direct method for equations of the neutral type |
scientific article; zbMATH DE number 6136681 |
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Nonmonotone functionals in the Lyapunov direct method for equations of the neutral type (English)
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15 February 2013
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In the framework of Lyapunov's direct method, the author presents twelve theorems on sufficient conditions for stability and asymptotic stability of the zero solution to the neutral-type equation in general form \[ \frac{d}{dt}D(t,x_t)=f(t,x_t),\;f(t,0)=0. \] The main feature of the approach is to use the so-called nonmonotone Lyapunov-Krasovskii functionals and Lyapunov-Razumikhin functions (see also [\textit{L. B. Knyazhishche}, Dokl. Nats. Akad. Nauk Belarusi 50, No. 5, 25--27 (2006; Zbl 1210.34102)]).
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delay equations of neutral type
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Lyapunov direct method
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stability
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asymptotic stability
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