MATHEMATICA BOHEMICA, Vol. 123, No. 3, pp. 301-316 (1998)

Remarks on generalized solutions of ordinary linear differential equations in the Colombeau algebra

Jan Ligeza

Jan Ligeza, Instytut Matematyki, Uniwersytet Slaski, Bankowa 14, 40-007 Katowice, Poland

Abstract: In this paper first order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in $ {\Cal G}^n (\Bbb R) $, where $ {\Cal G} (\Bbb R) $ denotes the Colombeau algebra.

Keywords: generalized ordinary differential equations, the Cauchy problem, distributions, Colombeau algebra

Classification (MSC2000): 34A10, 46F99

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