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| THE PERTURBATION OF ALMOST PERIODIC SOLUTION OF ALMOST PERIODIC SYSTEM |
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Citation： |
Lin Zhengsheng.THE PERTURBATION OF ALMOST PERIODIC SOLUTION OF ALMOST PERIODIC SYSTEM[J].Chinese Annals of Mathematics B,1984,5(3):363~373 |
| Page view： 709
Net amount： 781 |
Authors： |
Lin Zhengsheng; |
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| Abstract： |
By using the exponential dichotomy and the averaging methods a perturbation theory is established for the almost periodic solutions of an almost differential system.
Suppose that the almost periodic differential system
$$\[\frac{{dx}}{{dt}} = f(x,t) + {s^2}g(x,t,s)\begin{array}{*{20}{c}}
{}&{(1)}
\end{array}\]$$
has an almost periodic solution \[x = {x_0}(t,M)\] for s=0, where $\[M = ({m_1}, \cdots ,{m_k})\]$ is the
parameter vector. The author discusses the conditions under which (1) has an almost periodic solution $\[x = x(t,s)\]$ such that
$$\[\mathop {\lim }\limits_{s \to 0} x(t,s) = {x_0}(t,M)\]$$
holds uniformly. The results obtained are quite complete. |
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