The existence of the unique theorem of the solution refers to the existence and uniqueness of the equation under certain conditions, it is the most basic theorem in the theory of normal differential equations, has its great theoretical significance This paper is mainly to promote the existence of the unique theorem of the regular differential equation solution in the real domain. According to the theorem of the uniqueness of the solution in the real number domain and its proof and popularization, the principle of compression mapping is used to demonstrate the unique existence of the solution in the complex domain by using the analysis of the compression mapping principle through the change of known conditions such as lipsiz and Holder conditions.
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