A Dirichlet problem for the biharmonic equation in a semi-infinite strip

This paper addresses the two-dimensional biharmonic problem for a semi-infinite strip with Dirichlet boundary conditions. The method of superposition is used to solve the problem. The object of this paper is to clarify mathematical questions connected with the solution of a special integral equation and to provide a rigorous justification of the applicability of the method of superposition. Mellin's transform technique of investigating the asymptotic behaviour of unknown density when the argument tends to infinity is used.