TY - JOUR T1 - On the Solutions of a Fourth Order Difference Equation AU - Abo-zeıd, R PY - 2021 DA - June Y2 - 2021 DO - 10.32323/ujma.917838 JF - Universal Journal of Mathematics and Applications JO - Univ. J. Math. Appl. PB - Emrah Evren KARA WT - DergiPark SN - 2619-9653 SP - 76 EP - 81 VL - 4 IS - 2 LA - en AB - In this paper, we solve and study the global behavior of the well defined solutions of the difference equation $$x_{n+1}=\frac{x_{n}x_{n-3}}{Ax_{n-2}+Bx_{n-3}}, \quad n=0,1,...,$$ where $A, B>0$ and the initial values $x_{-i}$, $i\in\{0,1,2,3\}$ are real numbers. KW - difference equation KW - invariant set KW - forbidden set KW - convergence CR - [1] R. Abo-Zeid, On a fourth order rational difference equation, Tbilisi Math. J., 12 (4) (2019), 71-79. CR - [2] R. Abo-Zeid, Global behavior of a fourth order difference equation with quadratic term, Bol. Soc. Mat. Mexicana, 25 (2019), 187-194. CR - [3] R. Abo-Zeid, Global behavior of two third order rational difference equations with quadratic terms, Math. Slovaca, 69 (1) (2019), 147-158. CR - [4] R. Abo-Zeid, Behavior of solutions of a higher order difference equation, Alabama J. Math., 42 (2018), 1-10. CR - [5] R. Abo-Zeid, On the solutions of a higher order difference equation, Georgian Math. J., DOI:10.1515/gmj-2018-0008. CR - [6] R. Abo-Zeid, Forbidden sets and stability in some rational difference equations, J. Difference Equ. Appl., 24 (2) (2018), 220-239. CR - [7] R. Abo-Zeid, Global behavior of a higher order rational difference equation, Filomat 30(12) (2016), 3265􀀀3276. CR - [8] R. Abo-Zeid, Global behavior of a fourth order difference equation, Acta Comment. Univ. Tartu. Math., 18(2) (2014), 211-220. CR - [9] R. P. Agarwal and E. M. Elsayed, Periodicity and stability of solutions of higher order rational difference equation, Adv. Stud. Contemp. Math., 17 (2) (2008), 181–201. CR - [10] H. S. Alayachi, M. S. M. Noorani and E. M. Elsayed, Qualitative analysis of a fourth order difference equation, J. Appl. Anal. Comput., 10 (4) (2020), 1343–1354. CR - [11] A.M. Amleh, E. Camouzis and G. Ladas On the dynamics of a rational difference equation, Part 2, Int. J. Difference Equ., 3(2) (2008), 195-225. CR - [12] A.M. Amleh, E. Camouzis and G. Ladas On the dynamics of a rational difference equation, Part 1, Int. J. Difference Equ., 3(1) (2008), 1-35. CR - [13] F. Balibrea and A. Cascales, On forbidden sets, J. Difference Equ. Appl. 21(10) (2015), 974􀀀996. CR - [14] E. Camouzis and G. Ladas, Dynamics of Third Order Rational Difference Equations: With Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2008. CR - [15] H. El-Metwally and E. M. Elsayed, Qualitative study of solutions of some difference equations, Abstr. Appl. Anal., Volume 2012, Article ID 248291, 16 pages, 2012. CR - [16] M. G¨um¨us¸, The global asymptotic stability of a system of difference equations, J. Difference Equ. Appl., 24 (6) (2018), 976-991. CR - [17] M. Gu¨mu¨s¸ and O¨ . O¨ calan, Global asymptotic stability of a nonautonomous difference equation, J. Appl. Math., Volume 2014, Article ID 395954, 5 pages, 2014. CR - [18] E.A. Jankowski and M.R.S. Kulenovi´c, Attractivity and global stability for linearizable difference equations, Comput. Math. Appl. 57 (2009), 1592􀀀1607. CR - [19] C.M. Kent and H. Sedaghat, Global attractivity in a quadratic-linear rational difference equation with delay, J. Difference Equ. Appl., 15 (10) (2009), 913􀀀925. CR - [20] R. Khalaf-Allah, Asymptotic behavior and periodic nature of two difference equations, Ukrainian Math. J., 61 (6) (2009), 988-993. CR - [21] V. L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with applications, Kluwer Academic, Dordrecht, 1993. CR - [22] M. R. S. Kulenovi´c and M. Mehulji´c, Global behavior of some rational second order difference equations, Int. J. Difference Equ., 7 (2) (2012), 153–162. CR - [23] M.R.S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures, Chapman and Hall/HRC, Boca Raton, 2002. CR - [24] S. Stevic, Boundedness character of a fourth order nonlinear difference equation, Chaos, Sol. Frac., 40 (2009), 2364–2369. UR - https://doi.org/10.32323/ujma.917838 L1 - https://dergipark.org.tr/en/download/article-file/1711263 ER -