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The functional formulation of second-order ordinary differential equations

P. Chladek
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Abstract

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.

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P. Chladek. 2003-10-28. The functional formulation of second-order ordinary differential equations. https://arxiv.org/abs/math/0310443

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