Reconstruction of discontinuous Sturm-Liouville pencils with the eigenvalue in the boundary condition on the half-line

This work considers the discontinuous differential pencil on the half-line with the spectral boundary condition. We establish some uniqueness theorems on the potentials for the Sturm-Liouville pencil by the incomplete inverse problem and the interior inverse problem methods. We  determine the potentials by only a set of eigenvalues knowing the coefficients \beta_{۰},\beta_{۱},\beta_{۲},\beta_{۳} and potentials q_{۰}(x),q_{۱}(x) on (۰,a). We also establish the potentials by a set of values of eigenfunctions at some internal point x=a and eigenvalues.

کلیدواژه ها:

Inverse problem ، Sturm-Liouville pencil ، Spectral boundary condition ، Discontinuity