Sturm-Liouville Problems with Polynomially Eigenparameter Dependent Boundary Conditions

Year 2023, Volume: 27 Issue: 6, 1235 - 1242, 18.12.2023

Ayşe Kabataş

https://doi.org/10.16984/saufenbilder.1304365

Abstract

Sturm-Liouville equation on a finite interval together with boundary conditions arises from the infinitesimal, vertical vibrations of a string with the ends subject to various constraints. The coefficient (also called potential) function in the differential equation is in a close relationship with the density of the string. In this sense, the computation of solutions plays a rather important role in both mathematical and physical fields. In this study, asymptotic behaviors of the solutions for Sturm-Liouville problems associated with polynomially eigenparameter dependent boundary conditions are obtained when the potential function is real valued 𝑳𝟏- function on the interval (𝟎, 𝟏). Besides, the asymptotic formulae are given for the derivatives of the solutions.

Keywords

Sturm-Liouville problem, spectral parameter, pontential function, asymptotics

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