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 $X = \mathbb{R}^n$.
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- 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.