二阶常微分方程的泛函形式
The functional formulation of second-order ordinary differential equations
摘要：
本文给出了一类二阶常微分方程的完备解依赖于Neumann条件的充要条件。这些充要条件由F的函数方程和光滑可拓条件组成。说明性的例子来证明这一结果。在这些例子中，所提到的F的函数方程与测地线的函数方程、Jensen方程、圆锥曲线的函数方程和线性常微分方程的Neuman结果有关。
英文摘要：
In this paper, the necessary and sufficient conditions in order that a smooth mapping F be a dependence of a complete solution of some second-order ordinary differential equation on Neumann conditions are deduced. These necessary and sufficient conditions consist of functional equations for F and of a smooth extensibility condition. Illustrative examples are presented to demonstrate this result. In these examples, the mentioned functional equations for F are related to the functional equations for geodesics, to Jensen's equation, to the functional equations for conic sections and to Neuman's result for linear ordinary differential equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
