Distributional solution concepts for the Euler-Bernoulli beam equation with discontinuous coefficients

We study existence and uniqueness of distributional solutions w to the ordinary differential equation d(2)/dx(2)(a(x).(d(2)w(x)/dx(2)) + P(x)(d(2)w(x)/dx(2)) = g(x) 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 beat 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.