[Turkmath:6115] (no subject)

[Allaberen Ashyralyev]

Dear Colleagues!

You are cordially invited to the  Weekly Seminar “Analysis and Applied
Mathematics” on
  Date: Tuesday, May 16, 2023
Time: 12.00-13.00 (Istanbul) = 11.00-12.00 (Ghent) = 15.00-16.00 (Almaty)
Place: Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1
 Speaker: Dr. Yagub Aliyev
DA University, Baku - Azerbaijan
Title: Minimality conditions for Sturm-Liouville problems with a boundary
condition depending affinely or quadratically on an eigenparameter
Abstract: In the talk we will discuss Sturm-Liouville problems with a
boundary condition depending affinely or quadratically on an
eigenparameter: −𝑦′′ + 𝑞(𝑥)𝑦 = 𝜆y, 0 < 𝑥 < 1 (1) 𝑦′ (0) sin 𝛽 =
𝑦(0) cos 𝛽 , 0 ≤ 𝛽 < 𝜋 (2) 𝑦′ (1) = (𝑎𝜆^2 + 𝑏𝜆 + 𝑐)𝑦(1), (3)
where 𝜆 is the spectral parameter, 𝑞(𝑥) is a real valued and continuous
function on the interval [0,1], and 𝑎, 𝑏, 𝑐 are real. In the papers by
Binding, Browne, Watson, and Code the existence and asymptotics of
eigenvalues of (1)-(3) were studied. It was proved that the eigenvalues of
(1)-(3) form an infinite sequence, accumulating only at +∞, and the
following cases are possible: (a) All the eigenvalues are real and simple;
(b) All the eigenvalues are simple and all, except a conjugate pair of
non-real, are real; (c) All the eigenvalues are real and all, except one
double, are simple; (d) All the eigenvalues are real and all, except one
triple, are simple. The necessary and sufficient conditions for minimality
and completeness of the chosen system of root functions of the
corresponding operator were previously given in the form, which - 2 - uses
some special associated functions. In the current talk another method with
the direct use of characteristic functions will be discussed. This direct
method is known for the affine case and was extensively discussed in the
literature. The aim of the present paper is to develop this direct method
for the quadratic case and to consider the affine and quadratic cases
together in a unified way.

Abstracts and forthcoming talks can be found on our webpage
https://sites.google.com/view/aam-seminars
With my best wishes
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University,**34349**, Istanbul,
Turkiye**  and **Near East University, Lefkoşa(Nicosia), Mersin 10 Turkiye*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at eng.bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars
https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml
*icaam-online.org <http://icaam-online.org>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
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