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).
Highlights
She proved that the potential of the considered problem can be uniquely determined by a given dense subset of the zeros of the eigenfunctions called
1 Introduction We consider the boundary value problem L generated by the convolution-type Sturm– Liouville integro-differential operator x
Inverse nodal problems for different types of operators have been extensively well studied in several papers
Summary
She proved that the potential of the considered problem can be uniquely determined by a given dense subset of the zeros of the eigenfunctions called In 1989, Hald and McLaughlin studied more general boundary conditions and gave some numerical schemes for the reconstruction of the potential from a given dense subset of nodal points [2]. Inverse nodal problems for different types of operators have been extensively well studied in several papers (see [4,5,6,7,8,9,10,11,12,13,14] and [15]).
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