Qualitative analysis of eigenvalues and eigenfunctions of one boundary value-transmission problem

被引:15
作者
Aydemir, Kadriye [1 ]
Mukhtarov, Oktay S. [2 ,3 ]
机构
[1] Giresun Univ, Fac Educ, TR-28100 Giresun, Turkey
[2] Gaziosmanpasa Univ, Fac Arts & Sci, Dept Math, TR-60250 Tokat, Turkey
[3] Azerbaijan Natl Acad Sci, Inst Math & Mech, Baku, Azerbaijan
关键词
Sturm-Liouville problems; boundary-transmission conditions; eigenvalues; Fourier series of eigenfunctions; minimax principle; STURM-LIOUVILLE PROBLEMS; OPERATOR; DILATION;
D O I
10.1186/s13661-016-0589-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The aim of this study is to investigate various qualitative properties of eigenvalues and corresponding eigenfunctions of one Sturm-Liouville problem with an interior singular point. We introduce a new Hilbert space and integral operator in it such a way that the problem under consideration can be interpreted as a spectral problem of this operator. By using our own approaches we investigate such properties as uniform convergence of the eigenfunction expansions, the Parseval equality, the Rayleigh-Ritz formula, the minimax principle, and the monotonicity of eigenvalues for the considered boundary value-transmission problem (BVTP).
引用
收藏
页码:1 / 16
页数:16
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