Construction of asymptotic solutions of linear singularly disturbed second-order system with degenerations
The paper discusses the asymptotic behavior of the general solution of a linear singularly perturbed system $\varepsilon ^{2h} A(t,\varepsilon )\frac{{d^2 x}}{{dt^2 }} + \varepsilon ^h B(t,\varepsilon )\frac{{dx}}{{dt^2 }} + C(t,\varepsilon )x = 0,$  where x∈Rn, t∈[t0; T], h∈N, ε∈ (0, ε...
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| Datum: | 1992 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8040 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | The paper discusses the asymptotic behavior of the general solution of a linear singularly perturbed system
$\varepsilon ^{2h} A(t,\varepsilon )\frac{{d^2 x}}{{dt^2 }} + \varepsilon ^h B(t,\varepsilon )\frac{{dx}}{{dt^2 }} + C(t,\varepsilon )x = 0,$
 where x∈Rn, t∈[t0; T], h∈N, ε∈ (0, ε0], ε≪1 and det A(t, 0) ≡ 0. It is assumed that the quadratic pencil of matrices C(t, 0) + λB(t, 0) + λ2A(t, 0) is regular and has either simple “finite” and “infinite” elementary divisors or just one multiple elementary divisor. |
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