$napis="Abstract"; include "zacatek.inc"; ?> Preprint GA 5/2003
In this paper, the necessary and sufficient conditions in order that a smooth mapping $\ff(\ta,\al,\be,a,b)$ be a dependence of a complete solution $\x(\ta)$ of some second-order ordinary differential equation on Neumann conditions $\x(\al)=a$, $\x(\be)=b$, $\al \neq \be$ are deduced. These necessary and sufficient conditions consist of functional equations for $\ff$ and of a smooth extensibility condition. Illustrative examples are presented to demonstrate this result. In these examples, the mentioned functional equations for $\ff$ 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. include "konec.inc"; ?>