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P. Chladek

Publications and source records attributed to P. Chladek.

2 recordsLinked to original sources
arXiv2003

The Cauchy atlas on the manifold of all complete ODE solutions

In this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete solution of some differentiable first-order ordinary differential equation on the initial Cauchy condition are deduced. The result is obtained by studying the Cauchy atlas on a manifold of complete solutions. The proof is constructive - the corresponding differential equation is obtained. The autonomous case and the linear case are discussed. The relation to the Sincov functional equation is clarified.

math.CA↗
arXiv2003

The functional formulation of second-order ordinary differential equations

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.

math.CA↗