On covering mappings in generalized metric spaces in studying implicit differential equations
On covering mappings in generalized metric spaces in studying implicit differential equations
复制标题
论隐式微分方程研究中广义度量空间的映射
DOI：
10.13108/2020-12-4-41
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
W. Merchela
中科院分区：
文献类型：
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作者：
E. Zhukovskiy;W. Merchela
． 放一套？∅a度规？:哦?×?→[0，∞]被定义，而on ？h =∅a距离？:哦?×?→[0,∞]，它只满足恒等公理。我们定义了覆盖的概念和映射的Lipschitz性质？→?． 我们制定了保证解存在的条件？∈吗?到形式方程？(?？)= ?,吗?∈吗?的映射？:哦?×?→?，一个是覆盖变量，另一个是Lipschitz。利用这些条件研究了带偏差变量泛函方程的可解性和隐式微分方程的柯西问题的可解性。为了做到这一点，在空间上？勒贝格可测函数？：[0,1]→我们定义距离吗？每个连续函数在哪里？： R × R→[0，∞]满足？(?1、？2) = 0当且仅当？1 = ？2 ．
. Let on a set ? ̸ = ∅ a metric ? : ? × ? → [0 , ∞ ] be defined, while on ? ̸ = ∅ a distance ? : ? × ? → [0 , ∞ ] , be given, which satisfies only the identity axiom. We define the notion of covering and of Lipschitz property for the mappings ? → ? . We formulate conditions ensuring the existence of solutions ? ∈ ? to equations of form ? ( ?, ? ) = ?, ? ∈ ?, with a mapping ? : ? × ? → ?, being covering in one variable and Lipschitz in the other. These conditions are employed for studying the solvability of a functional equation with a deviation variable and of a Cauchy problem for an implicit differential equation. In order to do this, on the space ? of Lebesgue measurable functions ? : [0 , 1] → R we define the distance ? where each continuous function ? : R × R → [0 , ∞ ) satisfies ? ( ? 1 , ? 2 ) = 0 if and only if ? 1 = ? 2 .