以下为句子列表：
英文: The global inverse function theorem is applied for the existence and uniqueness of periodical solutions to the semilinear boundary value problems. Some results are improved.
中文: 摘要本文运用整体反函数理论证明了一类半线性方程边值问题周期解的存在唯一性，推广和改进了已有的一些结果。
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英文: This artcle in virtue of different mathematical methods of three kind, treats of three sides of unitary property about" x+ "question: Constructed intricate and dendriform frame of total C rebuke in virtue of inverse function of L. Collatz' s function;
中文: 本文运用三种不同的数学方法,论及 x+问题整体性质的三个方面: 利用柯拉茨函数的反函数,构造了全体C数列复杂的树状结构;
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