Abstract
We study existence and uniqueness of distributional solutions w to the ordinary differential equation with discontinuous coefficients and right-hand side. For example, if a and w are non-smooth the product a · w″ has no obvious meaning. When interpreted on the most general level of the hierarchy of distributional products discussed by Oberguggenberger, M. [1992, Multiplication of distributions and applications to partial differential equations (Harlow: Longman Scientific & Technical)], it turns out that existence of a solution w forces it to be at least continuously differentiable. Curiously, the choice of the distributional product concept is thus incompatible with the possibility of having a discontinuous displacement function as a solution. We also give conditions for unique solvability. §Supported by Ministry of Science of Serbia, project 144016, and the Austrian Science Fund (FWF) START program Y237 on ‘Nonlinear distributional geometry’.
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