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GLOBAL DYNAMICS OF A NON-AUTONOMOUS RATIONAL DIFFERENCE EQUATION
Ocalan, Ozkan The Korean Society for Computational and Applied M 2014 Journal of applied mathematics & informatics Vol.32 No.5
In this paper, we investigate the boundedness character, the periodic character and the global behavior of positive solutions of the difference equation $$x_{n+1}=p_n+\frac{x_n}{x_{n-1}},\;n=0,1,{\cdots}$$ where $\{p_n\}$ is a two periodic sequence of nonnegative real numbers and the initial conditions $x_{-1}$, $x_0$ are arbitrary positive real numbers.
GLOBAL DYNAMICS OF A NON-AUTONOMOUS RATIONAL DIFFERENCE EQUATION
Ozkan Ocalan 한국전산응용수학회 2014 Journal of applied mathematics & informatics Vol.32 No.5
In this paper, we investigate the boundedness character, the periodic character and the global behavior of positive solutions of the difference equation xn+1 = pn + xn/xn-1, n = 0,1 ... , where{pn}is a two periodic sequence of nonnegative real numbers and the initial conditions x-1, x0 are arbitrary positive real numbers.
SUFFICIENT OSCILLATION CONDITIONS FOR DYNAMIC EQUATIONS WITH NONMONOTONE DELAYS
OCALAN, OZKAN,KILIC, NURTEN The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.5-6
In this article, we analyze the first order delay dynamic equations with several nonmonotone arguments. Also, we present new oscillation conditions involving lim sup and lim inf for the solutions of these equations. Finally, we give an example to demonstrate the results.
Oscillations of Difference Equations with Several Terms
OCALAN, OZKAN 대한수학회 2006 Kyungpook mathematical journal Vol.46 No.4
In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation χ_(n+1) - χ_(n) + □P_(i)χ_(n-k_(i)), + qχ_(n-z) = 0, n = 0, 1, 2, ···, where p_(i) ∈ R, ki ∈ Z for i = 1, 2, · · · , m and z ∈ {-1, 0}. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation △^(r)χ_(n) + □P_(i)χ_(n-k_(i)) =0, n = 0,1,2,· · · , where p_(i) ∈ R, ki ∈ Z for i = 1, 2, · · · , m. The results are given terms of the p_(i), and the k_(i), for each i = 1, 2, ···, m.
Karpuz, Basak,Ocalan, Ozkan Korean Mathematical Society 2010 대한수학회보 Vol.47 No.2
In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form ${\nabla}_{\alpha}\;[x(t)\;-\;r(t)x(t\;-\;k)]\;+\;p(t)x(t\;-\;{\tau})\;-\;q(t)x(t\;-\;{\sigma})\;=\;0$, $t\;{\geq}\;t_0$, where $t_0\;{\in}\;\mathbb{R}$, t varies in the real interval ($t_0,\;{\infty}$), $\alpha$ > 0, $\kappa$, $\tau$, ${\sigma}\;{\geq}\;0$, $r\;{\in}\;C\;([t_0-{\alpha},\;{\infty}),\;\mathbb{R}^+$, p, $q\;{\in}\;C\;([t_0,\;{\infty}),\;\mathbb{R}^+)$ and ${\nabla}_{\alpha}x(t)\;=\;x(t)\;-\;x(t\;-\;{\alpha})$ for $t\;{\geq}\;t_0$.
Dynamical Behavior of a Third-Order Difference Equation with Arbitrary Powers
Gumus, Mehmet,Abo-Zeid, Raafat,Ocalan, Ozkan Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.2
The aim of this paper is to investigate the dynamical behavior of the difference equation $$x_{n+1}={\frac{{\alpha}x_n}{{\beta}+{\gamma}x^p_{n-1}x^q_{n-2}}},\;n=0,1,{\ldots}$$, where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-2}$, $x_{-1}$, $x_0$ are positive numbers. Also, some numerical examples are given to verify our theoretical results.