On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
-
Mounira Boulouh
and
Durhasan Turgut Tollu
ABSTRACT
In this work, we present results on the stability, the existence of periodic and oscillatory solutions of a general second order system of difference equations defined by the product of separable homogeneous functions of degree zero. Concrete systems for the obtained results are provided.
Funding statement: The first two authors acknowledge the support of the DGRSDT-MESRS-DZ in realizing the present work.
Acknowledgement
The authors thank the two referees for their comments and suggestions.
REFERENCES
[1] Amleh, A. M.—Grove, E. A.—Georgiou, D. A.—Ladas, G.: On the recursive seqience
[2] Border, K. C.: Euler’s Theorem for homogeneous functions, (2017); http://www.its.caltech.edu/~kcborder/Courses/Notes/EulerHomogeneity.pdf.Search in Google Scholar
[3] Boulouh, M.—Touafek, N.—Tollu, D. T.: On the behavior of the solutions of an abstract system of difference equations, J. Appl. Math. Comput. 68 (2022), 2937–2969.10.1007/s12190-021-01641-7Search in Google Scholar
[4] Elabbasy, E. M.—El-Metwally, H.—Elsayed, E. M.: On the difference equation
[5] Elabbasy, E. M.—Elsayed, E. M.: On the global attractivity of difference equation of higher order, Carpathian J. Math. 24(2) (2008), 45–53.Search in Google Scholar
[6] Elaydi, S.: An Introduction to Difference Equations. Undergraduate Texts in Math., Springer, 2005.Search in Google Scholar
[7] Halim, Y.—Touafek, N.—Yazlik, Y.: Dynamic behavior of a second-order nonlinearrational difference equation, Turk. J Math. 39 (2015), 1004–1018.10.3906/mat-1503-80Search in Google Scholar
[8] Kulenović, M. R. S.—Ladas, G.—Sizer, W. S.: On the recursive sequence
[9] Moaaz, O.—Chalishajar, D.—Bazighifan, O.: Some qualitative behavior of solutions of general class of difference equations, Mathematics 7 (2019), Art. No. 585.10.3390/math7070585Search in Google Scholar
[10] Taşdemir, E.: Global dynamics of a higher order difference equation with a quadratic term, J. Appl. Math. Comput. 67 (2021), 423–437.10.1007/s12190-021-01497-xSearch in Google Scholar
[11] Taşdemir, E.—Göcen, M.—Soykan, Y.: Global dynamical behaviours and periodicity of a certain quadratic-rational difference equation with delay, Miskolc Math. Notes 23(1) (2022), 471–484.10.18514/MMN.2022.3996Search in Google Scholar
[12] Touafek, N.: On a second order rational difference equation, Hacet. J. Math. Stat. 41 (2012), 867–874.Search in Google Scholar
[13] Touafek, N.—Halim, Y.: Global attractivity of a rational difference equation, Math. Sci. Lett. 2(3) (2013), 161–165.10.12785/msl/020302Search in Google Scholar
[14] Touafek, N.: On a general system of difference equations defined by homogeneous functions, Math. Slovaca 71(3) (2021), 697–720.10.1515/ms-2021-0014Search in Google Scholar
[15] Touafek, N.—Tollu, D. T.—Akrour, Y.: On a general homogeneous three-dimensional system of difference equations, Electron. Res. Arch. 29(5) (2021), 2841–2876.10.3934/era.2021017Search in Google Scholar
© 2023 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Remembering Professor Štefan Znám, 9.2.1936–17.7.1993
- Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures
- Enlargements of Quantales
- Multiplicative Dependent Pairs in the Sequence of Padovan Numbers
- Dirichlet Series with Periodic Coefficients, Riemann’s Functional Equation, and Real Zeros of Dirichlet L-Functions
- On the Rational Parametric Solution of Diagonal Quartic Varieties
- Theory of Certain Non-Univalent Analytic Functions
- Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)
- A Conjecture on H3(1) for Certain Starlike Functions
- Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces
- Complete Monotonicity and Inequalities Involving the k-Gamma and k-Polygamma Functions
- Study of Oscillation Criteria of Odd-Order Differential Equations with Mixed Neutral Terms
- On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
- On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces
- The Lehmann Type II Teissier Distribution
- Asymptotic Predictive Inference of Negative Lower Tail Index Distributions
- On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law
- The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds
Articles in the same Issue
- Remembering Professor Štefan Znám, 9.2.1936–17.7.1993
- Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures
- Enlargements of Quantales
- Multiplicative Dependent Pairs in the Sequence of Padovan Numbers
- Dirichlet Series with Periodic Coefficients, Riemann’s Functional Equation, and Real Zeros of Dirichlet L-Functions
- On the Rational Parametric Solution of Diagonal Quartic Varieties
- Theory of Certain Non-Univalent Analytic Functions
- Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)
- A Conjecture on H3(1) for Certain Starlike Functions
- Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces
- Complete Monotonicity and Inequalities Involving the k-Gamma and k-Polygamma Functions
- Study of Oscillation Criteria of Odd-Order Differential Equations with Mixed Neutral Terms
- On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
- On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces
- The Lehmann Type II Teissier Distribution
- Asymptotic Predictive Inference of Negative Lower Tail Index Distributions
- On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law
- The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds
