Inverse Spectral Problem for Integro-Differential Sturm–Liouville Operators with Discontinuity Conditions

We consider the Sturm–Liouville operator perturbed by a convolution integral on finite interval with Dirichlet boundary conditions and discontinuity in middle of interval. study inverse problem recovering term from spectrum. The is reduced to solving so-called main nonlinear equation singularity. To derive this equation, we do detailed analysis kernels transformation operators for integro-differential expression considered. prove global solvability which enables us uniqueness solution obtain necessary sufficient its terms asymptotics proof constructive gives an algorithm problem.