The Effect of the Singular Potential Functions for Eigenvalues of Sturm-Lıouville Operators

Abstract

In this article we obtain asymptotic formulas of arbitrary order for eigenfunctions and eigenvalues of thenon-self adjoint Sturm–Liouville operators with Dirichlet boundary conditions, when the potential is asummable function. Then using these we compute the main part of the eigenvalues in special cases. Theeigenvalues obtained by the asymptotic method and the eigenvalues obtained by the finite differencemethod followed by a numerical correction, are compared.