EIGENVALUE PROBLEMS FOR A CLASS OF STURM-LIOUVILLE OPERATORS ON TWO DIFFERENT TIME SCALES

被引：0
作者：
Durna, Zeynep [1 ]
Ozkan, A. Sinan [1 ]
机构：
[1] Cumhuriyet Univ, Fac Sci, Dept Math, TR-58140 Sivas, Turkey
来源：
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS | 2022年 / 71卷 / 03期
关键词：
  Dynamic equations; time scales; measure chains; eigenvalue problems; Sturm-Liouville theory; BOUNDARY-VALUE-PROBLEMS; DYNAMIC EQUATIONS; L-2; SPACES; POINT;
D O I：
10.31801/cfsuasmas.1036073
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this study, we consider a boundary value problem generated by the Sturm-Liouville equation with a frozen argument and with non-separated boundary conditions on a time scale. Firstly, we present some solutions and the characteristic function of the problem on an arbitrary bounded time scale. Secondly, we prove some properties of eigenvalues and obtain a formulation for the eigenvalues-number on a finite time scale. Finally, we give an asymptotic formula for eigenvalues of the problem on another special time scale: T = [alpha, delta 1] ? [delta 2, beta].
引用
收藏
页码：720 / 730
页数：11
相关论文
共 39 条
[1]   An interior inverse Sturm-Liouville problem on a time scale [J].
Adalar, Ibrahim ;
Ozkan, A. Sinan .
ANALYSIS AND MATHEMATICAL PHYSICS, 2020, 10 (04)
[2]   Dynamic equations on time scales: a survey [J].
Agarwal, R ;
Bohner, M ;
O'Regan, D ;
Peterson, A .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 141 (1-2) :1-26
[3]   Sturm-Liouville eigenvalue problems on time scales [J].
Agarwal, RP ;
Bohner, M ;
Wong, PJY .
APPLIED MATHEMATICS AND COMPUTATION, 1999, 99 (2-3) :153-166
[4]   Inverse spectral problems for non-local Sturm-Liouville operators [J].
Albeverio, S. ;
Hryniv, R. O. ;
Nizhnik, L. P. .
INVERSE PROBLEMS, 2007, 23 (02) :523-535
[5]   Schrodinger operators with nonlocal point interactions [J].
Albeverio, Sergio ;
Nizhnik, Leonid .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 332 (02) :884-895
[6]   Conformable fractional Sturm-Liouville problems on time scales [J].
Allahverdiev, Bilender P. ;
Tuna, Huseyin .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (04) :2299-2314
[7]   Investigation of the spectrum of singular Sturm-Liouville operators on unbounded time scales [J].
Allahverdiev, Bilender P. ;
Tuna, Huseyin .
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2020, 14 (01) :327-340
[8]  
ALLAHVERDIEV BP, 2020, UKR MATH J, V72, DOI DOI 10.37863/UMZH.V72I5.546
[9]   Eigenvalue distribution of second-order dynamic equations on time scales considered as fractals [J].
Amster, Pablo ;
De Napoli, Pablo ;
Pinasco, Juan Pablo .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 343 (01) :573-584
[10]   Detailed asymptotic of eigenvalues on time scales [J].
Amster, Pablo ;
De Napoli, Pablo ;
Pinasco, Juan Pablo .
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2009, 15 (03) :225-231
1234