Reconstruction of the Volterra-type integro-differential operator from nodal points

Abstract

In this work, the Sturm-Liouville problem perturbated by a Volterra-type integro-differential operator is studied. We give a uniqueness theorem and an algorithm to reconstruct the potential of the problem from nodal points (zeros of eigenfunctions).

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]).…”

Second Order Semilinear Volterra-Type Integro-Differential Equations with Non-Instantaneous Impulses

“…The theory and application of integrodifferential equations are important subjects in applied mathematics, see, for example [1][2][3][4][5][6][7][8] and recent development of the topic, see the monographs of [9]. In recent times there have been an increasing interest in studying the abstract autonomous second order, see for example [10][11][12][13][14].…”

Inverse Nodal Problems for Dirac-Type Integro-Differential System with Boundary Conditions Polynomially Dependent on the Spectral Parameter

“…Such operators have important applications in many …elds of science (see monographs [17], [36] and references therein). Therefore, many researchers are currently working on inverse problems for these operators ( [11], [12], [13], [14], [15], [19], [20], [22], [26] [27], [28], [30], [34] and [49]). The inverse nodal problem for Dirac type integro-di¤erential operators with Robin boundary conditions was …rst studied by [29].…”