Trace and inverse problem of a discontinuous Sturm–Liouville operator with retarded argument

In this study a discontinuous boundary value problem with retarded argument and with transmission conditions at the point of discontinuity is investigated. Regularized sums from the eigenvalues, oscillations of eigenfunctions and the solutions of inverse nodal problem for the problem are obtained. In the special case that the transmission coefficient δ = 1 and retarded argument Δ ≡ 0 in the results obtained below coincide with corresponding results in the classical Sturm–Liouville operator.