On First-Order Partial Differential Equations: An Existence Theorem and Its Applications
On First-Order Partial Differential Equations: An Existence Theorem and Its Applications
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一阶偏微分方程的存在性定理及其应用
DOI：
10.1007/978-981-10-0476-6_3
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Y. Hosoya
中科院分区：
文献类型：
--
作者：
Y. Hosoya
本文给出了一个标准一阶偏微分方程解的存在性与相应常微分方程解的可扩性之间的等价定理。此外，我们利用这一结果给出了偏微分方程解的存在性定理，并将该定理应用于消费者理论中的可积性问题。
In this paper, we present an equivalence theorem between the existence of a global solution of a standard first-order partial differential equation and the extendability of the solution of corresponding ordinary differential equation. Moreover, we use this result to produce existence theorems on partial differential equation, and apply this theorem to the integrability problem in consumer theory.