Asymptotic Analysis of Sturm-Liouville Problem with Dirichlet and Nonlocal Two-Point Boundary Conditions

Abstract

In this study, we obtain asymptotic expansions for eigenvalues and eigen-functions of the one-dimensional Sturm-Liouville equation with one classical Dirich-let type boundary condition and two-point nonlocal boundary condition. We analyze the characteristic equation of the boundary value problem for eigenvalues and de-rive asymptotic expansions of arbitrary order. We apply the obtained results to the problem with two-point nonlocal boundary condition.