一类具有拟算术均值的泛函微分方程

arXiv: Classical Analysis and ODEs Pub Date : 2020-05-17 DOI:10.29229/uzmj.2020-2-6

Shokhrukh Ibragimov

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摘要

本文描述了所有可微函数$\varphi,\psi\colon E\to\mathbb{R}$满足函数微分方程\begin{equation*} [\varphi(y) - \varphi(x)]\psi '\bigl(h(x,y)\bigr) = [\psi(y) - \psi(x)]\varphi '\bigl(h(x,y)\bigr), \end{equation*}对所有$x,y\in E$, $x本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On a functional-differential equation with quasi-arithmetic mean value

In this paper we describe all differentiable functions $\varphi,\psi\colon E\to\mathbb{R}$ satisfying the functional-differential equation \begin{equation*} [\varphi(y) - \varphi(x)]\psi '\bigl(h(x,y)\bigr) = [\psi(y) - \psi(x)]\varphi '\bigl(h(x,y)\bigr), \end{equation*} for all $x,y\in E$, $x

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arXiv: Classical Analysis and ODEs

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