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Periodic Solutions for a System of Difference Equations [PDF]

Discrete Dynamics in Nature and Society, 2009
This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory.
Shugui Kang, Bao Shi
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Periodic Solutions of a System of Nonlinear Difference Equations with Periodic Coefficients

Journal of Mathematics, 2020
This paper is dealt with the following system of difference equations xn+1=an/xn+bn/yn,yn+1=cn/xn+dn/yn, where n∈ℕ0=ℕ∪0, the initial values x0 and y0 are the positive real numbers, and the sequences ann≥0, bnn≥0, cnn≥0, and dnn≥0 are two-periodic and ...
Durhasan Turgut Tollu
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The Periodic Solutions of a Class of Difference Equations

Journal of Mathematics, 2022
In this paper, we study the periodic solutions of a class of difference equations and give a necessary and sufficient condition under which the nonnegative solutions of the equation converge to a 2k-periodic solution by using relevant theoretical ...
Qi Wang, Weiling You, Gengrong Zhang
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On Some Difference Equations with Eventually Periodic Solutions

Journal of Mathematical Analysis and Applications, 1998
The authors study the boundedness and the periodic character of the solutions of the equation \[ \begin{aligned} x_n & ={\alpha x_n +\beta x_{n-1} \over 2}, \quad \text{if }x_n+x_{n-1} \text{ is even}; \\ x_n & =\gamma x_n+ \partial x_{n-1}, \quad \text{if } x_n+x_{n-1} \text{ is odd, }n=0,1, \dots \end{aligned} \] where \(x_{-1}\), \(x_0\in Z\) and \(\
G Ladas
exaly   +3 more sources

Positive Periodic Solutions for Nonlinear Difference Equations with Periodic Coefficients

Journal of Mathematical Analysis and Applications, 1999
The authors consider the following boundary value problem \[ -\Delta [p(n-1)\Delta y(n-1)]+q(n) y(n)=f(n,y(n)), \quad n=1,2,\dots,N, \] \[ y(0)=y(N),\qquad p(0)\Delta y(0)=p(N)\Delta y(N). \] Using a fixed point theorem in cones, existence of one as well as two solutions is established for the boundary value problem.
Atici, FM, Guseinov, GS
exaly   +4 more sources

Periodic solutions of nonlinear second-order difference equations

Advances in Difference Equations, 2005
We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t+2)+by(t+1)+cy(t)=f(y(t)), where c≠0 and f:ℝ→ℝ is continuous.
Debra Lynn Etheridge, Jesús Rodriguez   +1 more
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Almost Periodic Solutions on a Class Secondorder Differential Equations with Piecewise Constant Argument

Journal of Harbin University of Science and Technology, 2019
Almost periodic solutions of differential equations are more general than periodic solutions, so almost periodic solutions will be studied on a class secondorder differential equations with piecewise constant argument.
YAO Hui-li, ZHANG Yue-jiao, HOU Sheng-nan   +2 more
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Periodic solutions of difference equations

Journal of Mathematical Analysis and Applications, 2003
For the difference equation \(x_{n+1}=\beta x_n- g(x_n)\) with \(\beta> 1\) and \(g(x)= \text{sign\,}x\) for \(x\neq 0\), \(g(0)= 1\), it is shown: For any \(m\in \mathbb{N}_0\) it has a \(2^m\)-periodic solution. If \(\beta^{2^m(2k+1)}- 2\beta^{2^m(2k-1)}\geq 1\) for \(k\in \mathbb{N}\) and some \(m\in\mathbb{N}\) it has a \((2k+1)2^m\)-periodic ...
Yi, Taishan, Zhou, Zhan
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Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay

Advances in Difference Equations, 2007
For periodic and almost periodic functional difference equations with finite delay, the existence of periodic and almost periodic solutions is obtained by using stability properties of a bounded solution.
Yihong Song
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Periodic solutions of periodic difference equations

Advanced Studies in Pure Mathematics, 2019
In this paper, we discuss the existence of periodic solutions of the periodic difference equation $$ x(n + 1) = f(n, x(n)),\ \ n \in \mathbf{Z} $$ and the periodic difference equation with finite delay $$ x(n + 1) = f(n, x_n),\ \ n \in \mathbf{Z}, $$ where $x$ and $f$ are $d$-vectors, and $\mathbf{Z}$ denotes the set of integers.
Furumochi, Tetsuo, Muraoka, Masato
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