以下为句子列表：
英文: An existence theorem concerning denumerable 1-homoclinic orbits and countable families of 1-periodic orbits was given under a generic condition; and an intuitionistic description about those orbits was also given.
中文: 证明在通有条件下，该异宿环附近存在可数无穷多条1-同宿轨，和可数无穷多个1-周期轨的单参数族，同时对这些周期轨和同宿轨作了直观描述。
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英文: An existence theorem of solution is established for a class of fourth-ordet two-point boundary value problems with all order derivatives by using integral equation and considering the heightof nonlinear term.
中文: 摘要通过运用积分方程并考察非线性项的“高度”对一类含有各阶导数的四阶两点边值问题建立了一个解的存在定理。
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英文: This article gives a new definition of complex integrating factor about first order ordinary differential equation and a new existence theorem of a type of integral factor and calculation formual, and the resuct in this paper amplifies the conclusions in
中文: 摘要本文推广了一阶微分方程复合型积分因子的概点，给出了复合型积分因子的存在定理和计算公式，所得结果涵盖并推广了相关文献的结论。
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英文: We present existence theorem for pseudo almost periodic solutions with piecewise constant argument by means of unique decomposite character and for pseudo almost periodic sequence solutions of relevent difference equations.
中文: 摘要利用伪概周期函数唯一分解性质，研究相关差分方程的伪概周期序列解，并以此为工具得出一类带逐段常变量微分方程伪概周期解的存在唯一性。
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