We prove the existence and uniqueness of the solution of the system.

证明了方程组解的存在性和唯一性。

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Under the suitable conditions, existence and uniqueness of the solution of the problem has been proved.

证明了该问题解的存在唯一性，有界性。

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At first, we will prove the local existence and uniqueness of the solution, and establish two comparison lemmas.

我们先证明问题解的局部存在性和唯一性，并建立两个比较引理。

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