Институт математики и математического моделирования

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 59

Date: Tuesday, May 5, 2026

Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 16.00-17.00 (Almaty)

Zoom link: https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09 ,

Conference ID: 667 827 0445, Access code: 1

Speaker:

Assoc. Prof. Dr. Yagub N. Aliyev

ADA University, Baku, Azerbaijan

Title: Sturm-Liouville problems with a boundary condition depending linearly on an eigenparameter

Abstract: This paper studies a Sturm-Liouville boundary value problem in which one of the boundary conditions depends linearly on the spectral parameter. The differential equation is considered on the interval with a classical boundary condition at one endpoint and an eigenparameter--dependent boundary condition at the other. Explicit formulas for the inner products and norms of eigenfunctions are obtained. These relations make it possible to analyze the structure of the system of root functions and the corresponding biorthogonal system. Using these results, the minimality of the system of root functions in L2(0,1) is established. Furthermore, the basis properties of the system of root functions in the spaces Lp(0,1), are investigated. Necessary and sufficient conditions under which the system forms a basis are derived. Special attention is given to the cases of multiple eigenvalues and the case when the eigenvalue coincides with the critical value -d/c. The obtained results reveal a symmetry between different spectral cases and provide a simpler approach that avoids the use of the exit spaces. Several examples are presented to illustrate the theoretical results.

Biography:

Yagub Aliyev is an Associate Professor at ADA University (Azerbaijan). His research interests include Sturm-Liouville theory, 3x+1 Problem, History of Mathematics, Number theory, Euclidean Geometry, Inequalities.

Abstracts and forthcoming talks can be found on our webpage

https://sites.google.com/view/aam-seminars

Kazakh Mathematical Journal

“Analysis and Applied Mathematics” Еженедельный онлайн семинар 59

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