The uniqueness of the solution of dual equations of an inverse indefinite Sturm-Liouville problem

In this paper we consider a linear second-order equation of Sturm-Liouville type: (I)y″+(λt−q(t))y=0,−1⩽t⩽1, with Dirichlet boundary conditions y(−1)=y(1)=0, where q is a positive sufficiently smooth function on [−1,1] and λ is a real parameter. We investigate the uniqueness of the solution for the dual equations of the indefinite inverse spectral problem (I). This result is necessary for expressing inverse problem of indefinite Sturm-Liouville equation.