Results 21 to 30 of about 649,859 (305)

Existence of meromorphic solutions of first order difference equations [PDF]

, 2018
It is shown that if It is shown that if \begin{equation}\label{abstract_eq} f(z+1)^n=R(z,f),\tag{\dag} \end{equation} where $R(z,f)$ is rational in $f$ with meromorphic coefficients and $\deg_f(R(z,f))=n$, has an admissible meromorphic solution ...
Korhonen, Risto, Zhang, Yueyang
core   +2 more sources

A rational difference equation

Computers & Mathematics with Applications, 2001
The authors investigate the nonlinear rational difference equation \[ x_{n+1}= (\alpha x_n+ \beta x_{n-1})/(A+x_{n-1}),\;n=0,1,2,\dots, \tag{*} \] where the parameters \(\alpha,\beta\) and \(A\) and the initial conditions \(x_{-1}\) and \(x_0\) are nonnegative real numbers.
Kulenović, M. R.S., Ladas, G., Prokup, N. R.   +2 more
openaire   +3 more sources

Global Behavior of a System of Second-Order Rational Difference Equations

Communications in Advanced Mathematical Sciences, 2021
In this paper, we consider the following system of rational difference equationsxn+1=a+xnb+cyn+dxn−1, yn+1=α+ynβ+γxn+ηyn−1, n=0,1,2,...xn+1=a+xnb+cyn+dxn−1, yn+1=α+ynβ+γxn+ηyn−1, n=0,1,2,...where a,b,c,d,α,β,γ,η∈(0,∞)a,b,c,d,α,β,γ,η∈(0,∞) and the ...
Phong Mai Nam
doaj   +1 more source

Global Behavior of Solutions to Two Classes of Second Order Rational Difference Equations [PDF]

, 2008
For nonnegative real numbers $\alpha$, $\beta$, $\gamma$, $A$, $B$ and $C$ such that $B+C>0$ and $\alpha+\beta+\gamma >0$, the difference equation \begin{equation*} x_{n+1}=\displaystyle\frac{\alpha +\beta x_{n}+\gamma x_{n-1}}{A+B x_{n}+C x_{n-1 ...
Basu, Sukanya, Merino, Orlando
core   +3 more sources

On a Competitive System of Rational Difference Equations

Universal Journal of Mathematics and Applications, 2019
This paper aims to investigate the global stability and the rate of convergence of positive solutions that converge to the equilibrium point of the system of difference equations in the modeling competitive populations in the form $$ x_{n+1}^{(1)}=\frac{
Mehmet Gümüş
doaj   +1 more source

Matrix difference equations for the supersymmetric Lie algebra sl(2,1) and the `off-shell' Bethe ansatz [PDF]

, 2000
Based on the rational R-matrix of the supersymmetric sl(2,1) matrix difference equations are solved by means of a generalization of the nested algebraic Bethe ansatz. These solutions are shown to be of highest-weight with respect to the underlying graded
Babujian H, Babujian H, Babujian H, Bassi Z S, Bassi Z S, Bracken A J, Faddeev L D, Foerster A, Frenkel I B, Göhmann F, Göhmann F, Korepin V E, Maassarani Z, Reshetikhin N Y, Scheunert M, Smirnov F A, T Quella, Zapletal A   +17 more
core   +3 more sources

Discrete Miura Opers and Solutions of the Bethe Ansatz Equations [PDF]

, 2004
Solutions of the Bethe ansatz equations associated to the XXX model of a simple Lie algebra come in families called the populations. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra. The proof is based on the
Alexander Varchenko, Bernshtein, Drinfeld, Evgeny Mukhin, Faddeev, Feigin, Mukhin, Ogievetsky, Semenov-Tian-Shansky   +8 more
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Bifurcation and Chaos Control of a System of Rational Difference Equations

Results in Nonlinear Analysis, 2021
We study a system of rational dierence equations in this article. For equilibrium points, we present the stability conditions. In addition, we show that the system encounters period-doubling bifurcation at the trivial equilibrium point O and Neimark ...
Rizwan Ahmed, Shehraz Akhtar, Muzammil Mukhtar, Faiza Anwar
doaj   +1 more source

Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms [PDF]

, 2007
We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension ...
A. Tamagawa, A.R. Magid, C. Bertolin, D. Goss, D.S. Thakur, E.R. Kolchin, F. Beukers, G. Böckle, G.W. Anderson, G.W. Anderson, G.W. Anderson, H. Matsumura, H. Matsumura, J. Fresnel, J. Yu, K.S. Kedlaya, L. Denis, M. Put van der, M. Put van der, M. Put van der, Matthew A. Papanikolas, O. Zariski, P. Deligne, P. Deligne, P. Ribenboim, S. Lang, S.K. Sinha, U. Hartl, W.C. Waterhouse, W.D. Brownawell, Y. André, Y. Taguchi   +31 more
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Global Behavior of Two Rational Third Order Difference Equations

Universal Journal of Mathematics and Applications, 2019
In this paper, we solve and study the global behavior of all admissible solutions of  the two difference equations $$x_{n+1}=\frac{x_{n}x_{n-2}}{x_{n-1}-x_{n-2}}, \quad n=0,1,...,$$ and $$x_{n+1}=\frac{x_{n}x_{n-2}}{-x_{n-1}+x_{n-2}}, \quad n=0,1 ...
R. Abo-zeid, H. Kamal
doaj   +1 more source