Solving of partial differential equations under minimal conditions

被引：0

作者：

Maslyuchenko, V. K. ^{[1
]}

Mykhaylyuk, V. V. ^{[1
]}

机构：

[1] Chernivtsi Natl Univ, Dept Appl Math, UA-58012 Chernovtsy, Ukraine

来源：

JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY | 2008年 / 4卷 / 02期

关键词：

seperately differentiable functions; partial differential equations;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is proved that a differentiable with respect to each variable function f : R-2 -> R is a solution of the equation partial derivative u/partial derivative x + partial derivative u/partial derivative y = 0 if and only if there exists a function phi : R -> R such that f(x,y) = phi(x-y). This gives a positive answer to a queation by R. Baire. Besides, this result is used to solve analogous partial differential equations in abstract spaces and partial differential equations of higher-order.

引用

页码：252 / 266

页数：15

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