Asymptotic analysis of Sturm–Liouville problem with nonlocal integral-type boundary condition

• Main Authors: Artūras Štikonas, Erdoğan Şen
• Format: Article
• Language: English
• Published: Vilnius University Press 2021-09-01
• Series: Nonlinear Analysis
• Subjects: Sturm–Liouville problem; nonlocal integral condition; asymptotics of eigenvalues and eigenfunctions
• Online Access: https://www.journals.vu.lt/nonlinear-analysis/article/view/24299

In this study, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the one-dimensional Sturm–Liouville equation with one classical-type Dirichlet boundary condition and integral-type nonlocal boundary condition. We investigate solutions of special initial value problem and find asymptotic formulas of arbitrary order. We analyze the characteristic equation of the boundary value problem for eigenvalues and derive asymptotic formulas of arbitrary order. We apply the obtained results to the problem with integral-type nonlocal boundary condition.