- Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Cilt: 27 Sayı: 6
- Sturm-Liouville Problems with Polynomially Eigenparameter Dependent Boundary Conditions
Sturm-Liouville Problems with Polynomially Eigenparameter Dependent Boundary Conditions
Authors : Ayşe KABATAŞ
Pages : 1235-1242
Doi:10.16984/saufenbilder.1304365
View : 176 | Download : 116
Publication Date : 2023-12-18
Article Type : Research
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