Remarks on the abstract form of nonlinear cauchy-kovalevsky theorems
Remarks on the abstract form of nonlinear cauchy-kovalevsky theorems
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DOI：
10.1080/03605307708820057
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发表时间：
1977
影响因子：
1.9
通讯作者：
M. S. Baouendi;C. Goulaouic
中科院分区：
文献类型：
--
作者：
M. S. Baouendi;C. Goulaouic
本文给出了非线性Cauchy-Kovalevsky定理在巴拿赫空间尺度上的一个抽象形式的新证明。[5]的证明是基于先前L. Nirenberg[4]使用的迭代方法，以稍微强一些的假设证明相同的结果。我们的证明基本上比[5]中给出的证明简单，并且依赖于在Banach空间的闭子集中定义的收缩映射的不动点的存在性。我们在本文中使用的权函数似乎与Nagumo[3]使用的权函数密切相关，而与[4]和t51中的权函数不同。
INTRODUCTION We give here a new proof of an abstract form of the nonlinear Cauchy-Kovalevsky theorem in a scale of Banach spaces given by T. Nishida€ 51. The proof of [5] is based on an iteration method used earlier by L. Nirenberg [4] to prove the same result with slightly stronger assumptions. Our proof is basically simpler than the one given in [5] and relies on the existence of a fixed point of a contraction mapping defined in a closed subset of a Banach space. The weight function we use in this paper seems to be closely related to the one used by Nagumo [3] and is different from the weight in [4] and t51.