A generalized solution in W2 1(0,1) of a problem concerning the deflection of a beam

A new method is proposed for formulating a boundary-value problem for a fourth-order ordinary differential equation with a solution in W₂ ¹(0, 1). This generalized formulation is based on a system of second-order equations with coefficients in W₂ ^–1 (0, 1). The existence and uniqueness of the indicated solution in this class is proven.Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 90–96, 1989.