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

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.
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