Asymptotic analysis of Sturm-Liouville problem with Dirichlet and nonlocal two-point boundary conditions

In this study, we obtain asymptotic expansions for eigenvalues and eigenfunctions of the one–dimensional Sturm–Liouville equation with one classical Dirichlet type boundary condition and two-point nonlocal boundary condition. We analyze the characteristic equation of the boundary value problem for e...

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Published in:Mathematical modelling and analysis Vol. 28; no. 2; pp. 308 - 329
Main Authors: Stikonas, Arturas, Sen, Erdogan
Format: Journal Article
Language:English
Published: Vilnius Vilnius Gediminas Technical University 21.03.2023
Subjects:
Asymptotic series
asymptotics of eigenvalues and eigenfunctions
Boundary conditions
Boundary value problems
Dirichlet condition
Dirichlet problem
Eigenvalues
Eigenvectors
Investigations
Liouville equations
Mathematical functions
Sturm–Liouville problem
two-point nonlocal conditions
asymptotics of eigenvalues and eigenfunctions
Sturm–Liouville problem
Dirichlet condition
two-point nonlocal conditions
ISSN:1392-6292, 1648-3510
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Abstract In this study, we obtain asymptotic expansions for eigenvalues and eigenfunctions of the one–dimensional Sturm–Liouville equation with one classical Dirichlet type boundary condition and two-point nonlocal boundary condition. We analyze the characteristic equation of the boundary value problem for eigenvalues and derive asymptotic expansions of arbitrary order. We apply the obtained results to the problem with two-point nonlocal boundary condition.
AbstractList In this study, we obtain asymptotic expansions for eigenvalues and eigenfunctions of the one–dimensional Sturm–Liouville equation with one classical Dirichlet type boundary condition and two-point nonlocal boundary condition. We analyze the characteristic equation of the boundary value problem for eigenvalues and derive asymptotic expansions of arbitrary order. We apply the obtained results to the problem with two-point nonlocal boundary condition.
In this study, we obtain asymptotic expansions for eigenvalues and eigenfunctions of the one-dimensional Sturm-Liouville equation with one classical Dirichlet type boundary condition and two-point nonlocal boundary condition. We analyze the characteristic equation of the boundary value problem for eigenvalues and derive asymptotic expansions of arbitrary order. We apply the obtained results to the problem with two-point nonlocal boundary condition. Keywords: Sturm-Liouville problem, Dirichlet condition, two-point nonlocal conditions, asymptotics of eigenvalues and eigenfunctions. AMS Subject Classification: 34B24; 34L20; 35R10.
Audience Academic
Author Štikonas, Artūras
Şen, Erdoğan
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10.1007/s11785-022-01202-1
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10.1007/978-94-011-3748-5
10.15672/HJMS.2017.494
10.1017/S0308210515000499
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10.3846/1392-6292.2009.14.229-246
10.1016/j.mcm.2011.07.039
10.1017/S0013091501001079
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10.15388/namc.2021.26.24299
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10.1007/s10986-007-0023-9
10.3846/1392-6292.2007.12.215-226
10.3846/mma.2021.13056
10.3846/13926292.2015.1116470
10.15388/NA.2014.3.1
10.1007/s10986-022-09577-6
10.7146/math.scand.a-15152
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10.3846/13926292.2001.9637157
10.1007/s10231-019-00934-w
10.1090/proc/15155
10.1155/2011/767024
10.1017/S030821050002521X
10.15388/NA.2019.5.5
10.3846/mma.2020.10787
10.2298/FIL1507671M
10.1088/0305-4470/39/14/004
10.15388/NA.2008.13.4.14552
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Sturm–Liouville problem
Dirichlet condition
two-point nonlocal conditions
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Snippet In this study, we obtain asymptotic expansions for eigenvalues and eigenfunctions of the one–dimensional Sturm–Liouville equation with one classical Dirichlet...
In this study, we obtain asymptotic expansions for eigenvalues and eigenfunctions of the one-dimensional Sturm-Liouville equation with one classical Dirichlet...
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StartPage 308
SubjectTerms Asymptotic series
asymptotics of eigenvalues and eigenfunctions
Boundary conditions
Boundary value problems
Dirichlet condition
Dirichlet problem
Eigenvalues
Eigenvectors
Investigations
Liouville equations
Mathematical functions
Sturm–Liouville problem
two-point nonlocal conditions
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