Spectral Characteristics of the Sturm-Liouville Problem with Spectral Parameter-Dependent Boundary Conditions

Year 2024, Issue: 48, 1 - 10, 30.09.2024

Aynur Çöl

https://doi.org/10.53570/jnt.1501326

Abstract

We consider the Sturm-Liouville problem on the half line $(0 \leq x<\infty)$, where the boundary conditions contain polynomials of the spectral parameter. We define the scattering function and present the spectrum of the boundary value problem. The continuity of the scattering function is discussed. In a special case, the Levinson-type formula is introduced, demonstrating that the increment of the scattering function's logarithm is related to the number of eigenvalues.

Keywords

Levinson-type formula, scattering function, spectral parameter dependent boundary condition

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