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
收藏
页码：252 / 266
页数：15
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