Asymptotic analysis of Sturm–Liouville problem with nonlocal integral-type boundary condition
Articles
Artūras Štikonas
Vilnius University
https://orcid.org/0000-0002-5872-5501
Erdoğan Şen
Tekirdag Namik Kemal University
https://orcid.org/0000-0001-6603-2652
Published 2021-09-01
https://doi.org/10.15388/namc.2021.26.24299
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Keywords

Sturm–Liouville problem
nonlocal integral condition
asymptotics of eigenvalues and eigenfunctions

How to Cite

Štikonas A. and Şen E. (2021) “Asymptotic analysis of Sturm–Liouville problem with nonlocal integral-type boundary condition”, Nonlinear Analysis: Modelling and Control, 26(5), pp. 969-991. doi: 10.15388/namc.2021.26.24299.

Abstract

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.

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