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| The Existence of Almost periodic Solutions of Singularly Perturbed Systems |
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Citation： |
Huang Yuanshi.The Existence of Almost periodic Solutions of Singularly Perturbed Systems[J].Chinese Annals of Mathematics B,1985,6(1):15~26 |
| Page view： 737
Net amount： 727 |
Authors： |
Huang Yuanshi; |
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| Abstract： |
First the author considers the system (1)$\frac{dx}{dt}=f(t,x,y,\varepsilon),\varepsilon\frac{dy}{dt}=g(t,x,y,\varepsilon)$ and its degenerate system (2)$\frac{dx}{dt}=f(t,x, y, 0), g(f, x, y, 0) =0$. In both noncritical and critical cases, sufficient conditions are established for the existence of almost periodic solutions of system (1) near the given solutions of system (2). The main method of proof is that, by performing suitable transformation, the author establishes exponential dichotomies, and then applies the theory of integral manifolds. Secondly, for the autonomous system (3)
$\frac{dx}{dt}=f(x,y,\varepsilon),\varepsilon\frac{dy}{dt}=g(x,y,\varepsilon)$, analogous results are obtained by performing the generalized normal coordinate transformation. |
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