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

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 asymp...

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Bibliographic Details
Published in:	Nonlinear analysis (Vilnius, Lithuania) Vol. 26; no. 5; pp. 969 - 991
Main Authors:	Štikonas, Artūras, Şen, Erdoğan
Format:	Journal Article
Language:	English
Published:	Vilnius University Press 01.09.2021
Subjects:	asymptotics of eigenvalues and eigenfunctions nonlocal integral condition Sturm–Liouville problem asymptotics of eigenvalues and eigenfunctions Sturm–Liouville problem nonlocal integral condition
ISSN:	1392-5113, 2335-8963
Online Access:	Get full text
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Summary:	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.
ISSN:	1392-5113 2335-8963
DOI:	10.15388/namc.2021.26.24299