Higher order regularized trace formula for the regular Sturm–Liouville equation contained spectral parameter in the boundary condition

Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument

“…The goal of this article is to calculate the regularized trace for the problem (1)- (5). We point out that our results are extension and/or generalization to those in [11][12][13][14][15][16][17][18][19][20][21]. For example, if the retardation 0   in (1) and ( ) 1, 1 at   then we have the formula of the first regularized trace for the classical Sturm-Liouville operator which is called Gelfand-Levitan formula (see [12]).…”

Identities for Eigenvalues of the Schrödinger Equation with Energy-Dependent Potential

“…Let ζ n , n ∈ Z, be the eigenvalues of (1) and (3). We can prove that the sequence {ζ n : n = 0, ±1, ±2, .…”

The regularized trace of Sturm–Liouville problem with discontinuities at two points

“…Then this work was continued by many authors ( see [1], [5][6][7][8], [12][13][14][15][16][17][18] and [20],respectively). A regularized trace formula for Sturm-Liouville equation with one or two boundary conditions depending on a spectral parameter was investigated in [2,4,6,11,22,24]. The regularized trace formula of the infinite sequence of eigenvalues for some version of a Dirichlet boundary value problem with turning points was calculated in [9].…”