The functional formulation of second-order ordinary differential equations
经典分析与常微分方程
2007-05-23 v1 动力系统
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.
引用
@article{arxiv.math/0310443,
title = {The functional formulation of second-order ordinary differential equations},
author = {P. Chladek},
journal= {arXiv preprint arXiv:math/0310443},
year = {2007}
}
备注
8 pages, Latex