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Mathematica Moravica
2019, vol. 23, br. 1, str. 11-25
Behavior of solutions of a second order rational difference equation
(naslov ne postoji na srpskom)
Abo-Zeid Raafat
The Higher Institute for Engineering & Technology, Department of Basic Science, Al-Obour, Cairo Egypt

e-adresa: abuzead73@yahoo.com
Ključne reči: 2010 Mathematics Subject Classification Primary: 39A20; Secondary: 39A21 Key words and phrases Difference equation; forbidden set; periodic solution; unbounded solution Full paper
Sažetak
(ne postoji na srpskom)
In this paper, we solve the difference equation xn+1 = α xnxn-1 - 1 , n = 0, 1, . . . , where α > 0 and the initial values x-1, x0 are real numbers. We find some invariant sets and discuss the global behavior of the solutions of that equation. We show that when α > 2 3 √ 3 , under certain conditions there exist solutions, that are either periodic or converging to periodic solutions. We show also the existence of dense solutions in the real line. Finally, we show that when α < 2 3 √ 3 , one of the negative equilibrium points attracts all orbits with initials outside a set of Lebesgue measure zero.
Reference

Abo-Zeid, R. (2017) On the solutions of a second order difference equation. Mathematica Moravica, vol. 21, br. 2, str. 61-73

Abo-Zeid, R. (2016) Global behavior of a higher order rational difference equation. Filomat, 30(12): 3265-3276

Abo-Zeid, R. (2014) Global behavior of a third order difference equation. Tamkang Journal of Mathematics, 43(3): 25-37

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Abo-Zeid, R. (2014) Global behavior of a rational difference equation with quadratic term. Mathematica Moravica, vol. 18, br. 1, str. 81-88

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Abo-Zeid, R. (2014) Global behavior of a fourth order difference equation. Acta et Commentationes Universitatis Tartuensis de Mathematica, 18(2): 211-211

Abo-Zeid, R. (2017) Global behavior of a fourth-order difference equation with quadratic term. Boletín de la Sociedad Matemática Mexicana, 25(1): 187-194

1

Abo-Zeid, R. (2014) Global behavior of a rational difference equation with quadratic term. Mathematica Moravica, vol. 18, br. 1, str. 81-88

Amleh, A.M., Camouzis, E., Ladas, G. (2008) On the dynamics of a rational difference equation. Inter. J. Difference Equ, Part 2, 3(2): 195-225

Amleh, A.M., Camouzis, E., Ladas, G. (2008) On the dynamics of a rational difference equation. Inter. J. Difference Equ, Part 1, 3(1): 1-35

Anisimova, A., Bula, I. (2014) Some problems of second-order rational difference equations with quadratic terms. Inter. J. Difference Equ, 9(1): 11-21

Bajo, I. (2014) Forbidden sets of planar rational systems of difference equations with common denominator. Applicable Analysis and Discrete Mathematics, 8(1): 16-32

1

Bajo, I., Liz, E. (2011) Global behaviour of a second-order nonlinear difference equation. Journal of Difference Equations and Applications, 17(10): 1471-1486

Bajo, I., Franco, D., Perán, J. (2011) Dynamics of a Rational System of Difference Equations in the Plane. Advances in Difference Equations, 2011(1): 958602-958602

Balibrea, F., Cascales, A. (2015) On forbidden sets. Journal of Difference Equations and Applications, 21(10): 974-996

Benedetto, J.J., Czaja, W. (2009) Integration and Modern Analysis. Basel: Birkhäuser

Bogachev, V.I. (2006) Measure Theory. Berlin: Springer Verlag, 1 & 2

Camouzis, E., Ladas, G. (2008) Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures. Boca Raton: Chapman & Hall

1

Dehghan, M., Kent, C.M., Mazrooei-Sebdani, R., Ortiz, N.L., Sedaghat, H. (2008) Dynamics of rational difference equations containing quadratic terms. Journal of Difference Equations and Applications, 14(2): 191-208

Halmos, P.R. (1974) Measure Theory. Berlin: Springer-Verlag

Janowski, E.J., Kulenović, M.R.S. (2009) Attractivity and global stability for linearizable difference equations. Computers & Mathematics with Applications, 57(9): 1592-1607

Kent, C.M., Sedaghat, H. (2009) Global attractivity in a quadratic-linear rational difference equation with delay. Journal of Difference Equations and Applications, 15(10): 913-925

Kocic, V.L., Ladas, G. (1993) Global Behavior of Nonlinear Difference Equations of Higher Order with Applications. Dordrecht: Kluwer Academic Publishers

Kocic, V.L., Ladas, G. (1993) Global Attractivity in a Second-Order Nonlinear Difference Equation. Journal of Mathematical Analysis and Applications, 180(1): 144-150

Kulenović, M.R.S., Mehuljić, M. (2012) Global behavior of some rational second order difference equations. Inter. J. Difference Equ, 7(2): 153-162

1

Kulenović, M.R.S., Ladas, G. (2002) Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures. Boca Raton: Chapman & Hall

Salamon, D.A. (2016) Measures and Integration. Zürich: ETH

Sedaghat, H. (2008) On third order rational equations with quadratic terms. J. Difference Equ. Appl, 14(8): 889-897

Shojaei, H., Parvandeh, S., Mohammadi, T., Mohammadi, Z., Mohammadi, N. (2011) Stability and convergence of a higher order rational difference equation. Austral. J. Bas. Appl. Sci, 5(11): 72-77

Szalkai, I. (2008) Avoiding forbidden sequences by finding suitable initial values. Inter. J. Difference Equ, 3(2): 305-315

Taylor, J.C. (1998) An Introduction to Measure and Probability. New Yourk: Springer-Verlag

Trench, W.F. (2002) Introduction to Real Analysis. Upper Saddle River, NJ: Prentice Hall
   

O članku

jezik rada: engleski
vrsta rada: izvorni naučni članak
DOI: 10.5937/MatMor1901011A
objavljen u SCIndeksu: 11.07.2019.
Creative Commons License 4.0

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