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Growth of Solutions of Homogeneous Differential–Difference Equations
Computer Sciences & Mathematics Forum, 2023 In this article, we study the growth properties of solutions of homogeneous linear differential–difference equations in the whole complex plane ∑j=0nAjzfjz+cj=0, n∈N+, where cj, j=0,...,n are complex numbers, and Aj(z), j=0, …, n are entire functions of ...
Hakima Lassal, Benharrat Belaϊdi
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The Chebyshev Difference Equation
Mathematics, 2020 We define and investigate a new class of difference equations related to the classical Chebyshev differential equations of the first and second kind.
Tom Cuchta +2 more
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On a Max-Type Difference Equation
Advances in Difference Equations, 2010 We prove that every positive solution of the max-type difference equation xn=max{A/xn-pα,B/xn-kβ}, n=0,1,2,… converges to x¯=max{A1/(1+α),B1/(1+β)} where p,k are positive integers, 0<
Ibrahim Yalcinkaya +2 more
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2008 Construction stochastic difference equations connecting results of supervision of instant values of dynamic processes described by special equation Ricatti, is considered.
A. S. Ovsienko +1 more
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The generalized hypergeometric difference equation
Demonstratio Mathematica, 2018 A difference equation analogue of the generalized hypergeometric differential equation is defined, its contiguous relations are developed, and its relation to numerous well-known classical special functions are demonstrated.
Bohner Martin, Cuchta Tom
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Difference–Differential Equations [PDF]
Nature, 1948 THE general linear homogeneous difference–differential equation with constant coefficients is where 0 ⩽ μ ⩽m, 0⩽ν ⩽ n, y(ν)(t) is the ν-th derivative of the unknown function y (t) and 0 = b0 bm, if amn≠ 0. (2) Was first given by Hilb8, but under conditions which would exclude most of the applications.
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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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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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