Open AccessAsymptotic analysis of Sturm–Liouville problem with nonlocal integral-type boundary condition
Author(s) -
Artūras Štikonas,
Erdoğan Şen
Publication year - 2021
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/namc.2021.26.24299
Subject(s) - mathematics , boundary value problem , eigenvalues and eigenvectors , mathematical analysis , eigenfunction , sturm–liouville theory , dirichlet boundary condition , type (biology) , mixed boundary condition , robin boundary condition , dirichlet distribution , integral equation , order (exchange) , physics , ecology , finance , quantum mechanics , economics , biology
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.