【摘要】 本文讨论Ｂａｎａｃｈ空间中的Ｃａｕｃｈｙ问题解的存在性定理。证明了Ｃａｕｃｈｙ方程右端函数ｆ（·）为ｋ－集压缩映象时，Ｃａｕｃｈｙ问题的解必存在，从而，将通常要求ｆ（·）满足Ｌｉｐ条件或绝对连续这两种条件统一起来，并加以推广。更多还原

【Abstract】 In this paper, We discuss existence theorem for Cauchy problems on Banach space. We prove that if the right hand side function f(·) is a k set compression mapping, then there exists solution for Canchy problem. Therefore, the conditions that f(·) satisfying Lip condition or f(·) being absolute continuous are unifide and extended.更多还原