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Equations with first-order partial derivatives in the class of distinctly $L$-differentiable functions
Myronyk Vadym 1 , Mykhaylyuk Volodymyr 2,3
1 Department of Algebra and Informatics, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
2 Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
3 Jan Kokhanowski University, Kielce, 25-001, Poland
Keywords: еquations with first-order partial derivatives, $L$ -differentiable functions
Abstract

We obtain a general representation $f(x,y) = φ(u(x) - y)$ for solutions $f : X^2 → Z$  of the differential equation $Df_y(x)(h) + Df^x(y) (Du(h)) = 0,$ where $D$ is the differentiation operator and $u : X → X$  is a differentiable operator of tensor type, in the class of separately differentiable continuous mappings and in the case $X = \mathbb{R}^n$.

References

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Cite
ACS Style
Myronyk, V.; Mykhaylyuk, V. Equations with first-order partial derivatives in the class of distinctly $L$-differentiable functions. Bukovinian Mathematical Journal. 2016, 3
AMA Style
Myronyk V, Mykhaylyuk V. Equations with first-order partial derivatives in the class of distinctly $L$-differentiable functions. Bukovinian Mathematical Journal. 2016; 3(3-4).
Chicago/Turabian Style
Vadym Myronyk, Volodymyr Mykhaylyuk. 2016. "Equations with first-order partial derivatives in the class of distinctly $L$-differentiable functions". Bukovinian Mathematical Journal. 3 no. 3-4.
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