Infinite systems for a biharmonic problem in a rectangle: discussion of non–uniqueness
A. M. J. Davis · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2003
Meleshko & Gomilko, referred to below as MG, developed a systematic technique, based on Mellin transforms, for analysing the infinite systems that occur in various biharmonic problems for the rectangular domain. By estimating the asymptotic behaviour of the solution sequences, the convergence of the series is considerably improved, even at the corner points. However, MG overlooked the existence of solutions of the homogeneous systems, the consequent non–uniqueness and the need to satisfy solvability conditions in order for the solutions to exist. Fortunately, their main results remain valid and so the brief discussion here is aimed at elucidating the structures of the systems.