全局线性柯西问题

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-09-24 DOI:10.1016/j.bulsci.2025.103740

Faiza Derrab

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引用次数: 0

摘要

本文主要研究傅氏柯西问题。在一类函数Ck， k∈N∪{∞}的空间中，建立了一个解对Fuchsian变量的整体存在唯一性，对其他变量的整体存在唯一性。利用不动点定理在由合适的主函数定义的Banach空间中的应用，给出了不动点定理的证明方法。

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Global linear Cauchy problem

This paper is devoted to the study of the Fuchsian Cauchy problem. We establish the global existence and uniqueness of a solution in spaces of functions of class

C^{k}

k \in N \cup {\infty}

, with respect to the Fuchsian variable and entire with respect to the other variables. The method of proof is based on the application of the fixed point theorem in some Banach spaces defined by suitable majorant functions.

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