Existence of Solutions of an Ill-Posed Problem for the Vibrating String
L. Lorne Campbell · Canadian Mathematical Bulletin · 1982
Abstract The Dirichlet problem is examined for the vibrating string equation on a rectangle with commensurable sides. As is well-known, a solution, if it exists, is not unique. A necessary and sufficient condition is obtained on the boundary values for existence of solutions. A simple formula for the solution is obtained.