Asymptotic Properties of Solutions to Discrete Sturm-Liouville Monotone Type Equations-Reference-Cited by-同舟云学术

Asymptotic Properties of Solutions to Discrete Sturm-Liouville Monotone Type Equations

Published:2023-06-01 Issue:2 Volume:84 Page:35-44
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Migda Janusz¹,Schmeidel Ewa²

Affiliation:

1. 1 Faculty of Mathematics and Computer Science , Adam Mickiewicz University , Poznań , Poland

2. 2 Institute of Computer Science , University of Bialystok , Białystok , Poland

Abstract

Abstract We investigate the discrete equations of the form Δ ( r n Δ x n ) = a n f ( x σ ( n ) ) + b n .

\Delta \left( {{r_n}\Delta {x_n}} \right) = {a_n}f\left( {{x_{\sigma \left( n \right)}}} \right) + {b_n}.

Using the Knaster-Tarski fixed point theorem, we study solutions with prescribed asymptotic behaviour. Our technique allows us to control the degree of approximation. In particular, we present the results concerning harmonic and geometric approximations of solutions.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2023-0014

Reference15 articles.

1. AGARWAL, R. P.: Difference Equations and Inequalities: Theory, Methods and Applications. Marcel Dekker, New York, 2000.

2. AHLBRANDT, C. D.—PETERSON, A. C.: Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations. Kluwer Academic Publishers, Boston, 1996.

3. AMREIN, W. O.—HINZ, A. M.—PEARSON, D. B.: (eds.), Sturm-Liouville theory. Past and present. (Selected survey articles based on lectures presented at a colloquium and workshop in Geneva, Italy, September 15–19, 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm.) Birkhüser Verlag, Basel, 2005.

4. CHENG, S. S.—LI, J.—PATULA, W. T.: Bounded and zero convergent solutions of second-order difference equations, J. Math. Anal. Appl. 141 (1989), no. 2, 463–483. DOI: 10.1016/0022-247X(89)90191-1

5. HILSCHER, R.Š.: Spectral and oscillation theory for general second order Sturm--Liouville difference equations, Adv. Difference Equ. 2012, paper no. 82, (2012), 19 pp.