Bilender P Allahverdiev, HÜSEYİN TUNA

DOI Number
First page
Last page


In this paper, we consider an impulsive Sturm-Lioville problem on Sturmian time scales. We investigate the existence and uniqueness of the solution of this problem. We study some spectral properties and self-adjointness of the boundary-value problem. Later, we construct the Green function for this problem. Finally, an eigenfunction expansion is obtained.


Impulsive Sturm–Liouville problems, maximal and minimal operators, Green’s function, self-adjoint operator, eigenfunction expansion

Full Text:



R. P. Agarwal, M. Benchohra, D. O’Regan and A. Ouahab: Second order impulsive dynamic equations on time scales, Funct. Differ. Equ. 11 (2004), 223-234.

C. Ahlbrandt, M. Bohner and T. Voepel: Variable change for Sturm–Liouville differential expressions on time scales. Journal of Difference Equations and Applications. 9 (1) (2003), 93-107.

Z. Akdogan, M. Demirci and O. Sh. Mukhtarov: Green function of discontinuous boundary value problem with transmission conditions, Math. Meth. Appl. Sci. 30 (2007). 1719-1738.

B. P. Allahverdiev and H. Tuna: Investigation of the spectrum of singular Sturm–Liouville operators on unbounded time scales. S˜ao Paulo J. Math. Sci. 14 (2020), 327-340.

B. P. Allahverdiev and H. Tuna: Conformable fractional dynamic dirac system. Ann Univ Ferrara (2022).

B. P. Allahverdiev and H. Tuna: Conformable fractional Sturm–Liouville problems on time scales. Math Meth Appl Sci. 45 (2022), 2299– 2314

F. M. Atici and G. Sh. Guseinov: On Green’s functions and positive solutions for boundary value problems on time scales. J. Comput. Appl. Math. 141 (1-2) (2002), 75-99.

M. Benchohra, S. K. Ntouyas and A. Ouahab: Existence results for second order boundary value problem of impulsive dynamic equations on time scales. J. Math. Anal. Appl. 296 (2004), 69-73.

M. Benchohra, J. Henderson and S. Ntouyas: Impulsive Differential Equations and Inclusions, vol. 2 of Contemporary Mathematics and Its Applications, Hindawi Publishing Corporation, New York, NY, USA, 2006.

M. Bohner and A. Peterson: Dynamic Equations on Time Scales, Birkhauser, Boston, 2001.

M. Bohner and A. Peterson (Eds.): Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.

T. Gulsen, S. M. Sian, E. Yilmaz and H. Koyunbakan: Impulsive diffusion equation on time scales. Int. J. Anal. Appl. 16 (1) (2018), 137-148.

S. Hilger: Analysis on measure chains–a unified approach to continuous and discrete calculus. Results Math. 18 (1990), 18-56.

A. N. Kolmogorov and S. V Fomin: Introductory Real Analysis, Translated by R.A. Silverman, Dover Publications, New York, 1970.

Q. Kong and Q. R. Wang: Using time scales to study multi-interval Sturm–Liouville problems with interface conditions. Results. Math. 63 (2013), 451-465.

V. Lakshmikantham, D. D. Bainov and P. S. Simeonov: Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics,World Scientific, Teaneck, NJ, USA, 1989.

K. R. Mamedov and N. Palamut: On a direct problem of scattering theory for a class of Sturm–Liouville operator with discontinuous coefficient. Proc. Jangjeon Math. Soc. 12 (2) (2009), 243-251.

O. Sh. Mukhtarov and K. Aydemir: The eigenvalue problem with Interaction conditions at one interior singular point. Filomat. 31 (17) (2017), 5411-5420.

M. A. Naimark: Linear Differential Operators, 2nd edn., Nauka, Moscow,1969; English transl. of 1st. edn., 1,2, New York, 1968.

A. S. Ozkan and I. Adalar: Half-inverse Sturm–Liouville problem on a time scale. Inverse Probl. 36 (2) (2020), Article ID 025015, 8 p.

A. M. Samoilenko and N. A. Perestyuk: Impulsive Differential Equations, vol. 14 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific, River Edge, NJ, USA, 1995.



  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)