Sturm-Liouville Problems with Polynomially Eigenparameter Dependent Boundary Conditions

Authors : Ayşe Kabataş

Pages : 1235-1242

Doi:10.16984/saufenbilder.1304365

View : 211 | Download : 132

Publication Date : 2023-12-18

Article Type : Research Paper

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 ????????- function on the interval (????, ????). Besides, the asymptotic formulae are given for the derivatives of the solutions.
Keywords : Sturm Liouville problem, spectral parameter, pontential function, asymptotics