Inverse problem of the Boussinesq–Love equation with an extra integral condition

The paper addresses an inverse boundary value problem for the Boussinesq–Love equation with an extra integral condition of the first kind. The problem is firstly reduced to the problem that is in a sense quivalent to the original. Then, the Fourier mathod is applied, reducing the problem to solution of a system of integral equations. The existence and uniqueness of the latter equation is proved by the contraction mapping principle, which also yoelds the unique solution of the equivalent problem. Using equivalence, we finally prove the unique existence of a classical solution of the problem under consideration.