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

Boundary value problems

Oktay S Mukhtarov¹  Kadriye Aydemir² 

[1] Department of Mathematics, Faculty of Arts and Science, GaziosmanpaşFaculty of Education, Giresun University, Giresun, Turkey;a University, Tokat, Turkey

关键词: Sturm-Liouville problems;    boundary-transmission conditions;    eigenvalues;    Fourier series of eigenfunctions;    minimax principle;   

DOI  :  10.1186/s13661-016-0589-4

学科分类：数学（综合）

来源: SpringerOpen

【 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).

【 授权许可】

CC BY