Results 11 to 20 of about 3,599,122 (270)
On a nonlinear second-order difference equation
Journal of Inequalities and Applications, 2022 We study a nonlinear second-order difference equation which considerably extends some equations in the literature. Our main result shows that the difference equation is solvable in closed form. Some applications of the main result are also given.
Stevo Stević +3 more
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A Difference Equation Model of Infectious Disease [PDF]
International Journal Bioautomation, 2022 In the context of so much uncertainty with coronavirus variants and official mandate based on seemingly exaggerated predictions of gloom from epidemiologists, it is appropriate to consider a revised model of relative simplicity, because there can be ...
Anthony Shannon +3 more
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On a Max-Type Difference Equation
Discrete Dynamics in Nature and Society, 2007 We study the behaviour of the solutions of the following difference equation with the max operator: xn+1=max{1/xn,Axn−1}, n∈ℕ0, where parameter A∈ℝ and initial values x−1 and x0 are nonzero real numbers.
I. Yalçinkaya +2 more
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Some representations of the general solution to a difference equation of additive type
Advances in Difference Equations, 2019 The general solution to the difference equation xn+1=axnxn−1xn−2+bxn−1xn−2+cxn−2+dxnxn−1xn−2,n∈N0, $$x_{n+1}=\frac {ax_{n}x_{n-1}x_{n-2}+bx_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n}x_{n-1}x_{n-2}},\quad n\in\mathbb{N}_{0}, $$ where a,b,c∈C $a, b, c\in\mathbb{C}$, d∈
Stevo Stević
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Dynamics of a Rational Difference Equation
Advances in Difference Equations, 2010 The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn+1=(α+βxn+γxn-k)/(1+xn-k), n∈ℕ0, where the parameters
Wan-Tong Li, Lin-Xia Hu, Xiu-Mei Jia
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On the Difference Equation xn+1=xnxn-k/(xn-k+1a+bxnxn-k)
Abstract and Applied Analysis, 2012 We show that the difference equation xn+1=xnxn-k/xn-k+1(a+bxnxn-k),n∈ℕ0, where k∈ℕ, the parameters a, b and initial values x-i, i=0,k̅ are real numbers, can be solved in closed form considerably extending the results in the literature.
Stevo Stević +3 more
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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
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A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials [PDF]
, 2009 A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials ...
Abramowitz M. +10 more
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Well-posedness of difference elliptic equation
Discrete Dynamics in Nature and Society, 1997 The exact with respect to step h∈(0,1] coercive inequality for solutions in Ch of difference elliptic equation is established.
Pavel E. Sobolevskii
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Representation of solutions of a solvable nonlinear difference equation of second order
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We present a representation of well-defined solutions to the following nonlinear second-order difference equation $$x_{n+1}=a+\frac{b}{x_n}+\frac{c}{x_nx_{n-1}},\quad n\in\mathbb{N}_0,$$ where parameters $a, b, c$, and initial values $x_{-1}$ and $x_0 ...
Stevo Stevic +3 more
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