Sturm-Liouville Problems with Polynomially Eigenparameter Dependent Boundary Conditions

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.