A regularized trace formula and oscillation of eigenfunctions of a Sturm-Liouville operator with retarded argument at 2 points of discontinuity

Abstract

In this study, first, a formula for regularized sums of eigenvalues of a Sturm-Liouville problem with retarded argument at 2 points of discontinuity which contains a spectral parameter in the boundary conditions is obtained. After that, oscillation properties of the related problem is investigated. Finally, under the condition that a subset of nodal points is dense in definition set, the potential function is determined.