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Remarks on generalized solutions to linear ordinary differential equations in the Colombeau algebra. (English) Zbl 0937.34003
Summary: First-order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in \( {\mathcal G}^n (\mathbb{R}) \), where \( {\mathcal G} (\mathbb{R}) \) denotes the Colombeau algebra.

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
46F99 Distributions, generalized functions, distribution spaces
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