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This article is cited in 1 scientific paper (total in 1 paper)
Problem of instability in the first approximation
V. E. Slyusarchuk Novopolotsk Polytechnic Institute
Abstract:
Let $E$ be a Banach space, $A$ be a continuous linear operator such that $\sigma(A)\cap\{\lambda: \mathrm{Re}\,\lambda>0\}\ne\varnothing$, and $F(t, x)$ be a continuous function on $[0,\infty)\times E$ satisfying the condition $||F(t, x)||\leqslant q||x||$ ($q=\mathrm{const}$). An example of a system ${dx}/{dt}=Ax+F(t, x)$ is given which has an exponentially stable zero solution for certain $F(t, x)$ with arbitrarily small $q$.
Received: 17.06.1975
Citation:
V. E. Slyusarchuk, “Problem of instability in the first approximation”, Mat. Zametki, 23:5 (1978), 721–723; Math. Notes, 23:5 (1978), 398–399
Linking options:
https://www.mathnet.ru/eng/mzm10000 https://www.mathnet.ru/eng/mzm/v23/i5/p721
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Abstract page: | 128 | Full-text PDF : | 51 | First page: | 1 |
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