In case the coefficients are periodic, we give some sufficient conditions for the existence and uniqueness of asymptotic periodic solution.

对于系数具有周期性时，我们给出了渐进周期解存在并且唯一的必要条件。

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Gaussian beam is the asymptotic solution of wave equation concentred at the central ray.

高斯束是波动方程在特定射线附近的高频渐近解。

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Under the appropriate conditions, the asymptotic solution and its existence conditions are obtained, the results for a class of quasi-circular membrane oscillation problem is extended.

在适当的条件下，得出了这类问题的渐近解及其可解性条件，推广了一类近乎圆膜的振动问题所得的结果。

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