A note on the nonuniqueness of the Boussinesq–Galerkin solution in elastic theory

Based on the two new theorems, the nonuniqueness of the Boussinesq–Galerkin solution is studied, and then the scope of the nonuniqueness is discussed. In previous works of Cheng, and Barrett and Ellis, they claimed that the Boussinesq–Galerkin solution is nonunique, through using some assumptions to simplify the expressions of displacement functions. However, it should be pointed out that these authors did not provide convincing arguments to support their assumptions. In present work, we give a rigorous reasoning process to show the nonuniqueness of the Boussinesq–Galerkin solution, and then discuss the validity of the assumptions of Cheng, and Barrett and Ellis.