Results 31 to 40 of about 14,780,959 (374)
On the discrete and continuous Miura Chain associated with the Sixth Painlevé Equation [PDF]
, 1999 A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or B\"acklund transformations. We describe such a chain for the sixth Painlev\'e equation (\pvi), containing, apart from \pvi itself, a Schwarzian ...
Ablowitz +25 more
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On a Higher-Order Difference Equation
Discrete Dynamics in Nature and Society, 2010 We describe in an elegant and short way the behaviour of positive solutions of the higher-order difference equation xn=cxn−pxn−p−q/xn−q, n∈ℕ0, where p,q∈ℕ and c>0, extending some recent results in the literature.
Bratislav D. Iričanin, Wanping Liu
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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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Hyers-Ulam stability of Pielou logistic difference equation
, 2017 We investigate Hyers-Ulam stability of the first order difference equation xi+1 = axi+b cxi+d , where ad− bc = 1, c 6= 0 and |a+ d| > 2. It has Hyers-Ulam stability if the initial point x0 lies in some definite interval of R.
Soon-Mo Jung, Y. Nam
semanticscholar +1 more source
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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ON SOLVABILITY OF ONE DIFFERENCE EQUATION
Проблемы анализа, 2017 We consider a system of difference equation similar to those that appear as description of cumulative sums. Using Hamel bases, we construct pathological solutions to this system for constant right-hand sides.
I. A. Chernov
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Hyers-Ulam stability of elliptic Möbius difference equation
, 2017 The linear fractional map on the Riemann sphere with complex coefficients is called Möbius map. If satisfies , then is called elliptic Möbius map. Let be the solution of the elliptic Möbius difference equation for every . We show that the sequence on the
Y. Nam
semanticscholar +1 more source
AIMS Mathematics, 2023 We give detailed theoretical explanations for getting the closed-form formulas and representations for the general solutions to four special cases of a class of nonlinear difference equations of second order considered in the literature, present an ...
Stevo Stević
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Differential-difference equations reducible to difference and q-difference equations
Computers & Mathematics with Applications, 2001 Asymptotic properties of solutions of the differential-difference equation \[ x'(qt+1)=h(x(t))x'(t), \quad t\geq 0,\;q\geq 1 \tag{*} \] are investigated. Let \(\varphi\in C^1([0,1];\mathbf R)\) satisfies \(\varphi'(1)=h(\varphi(0))\varphi'(0)\). A solution \(x\) of (*) satisfying \(x(t)=\varphi(t)\), \(t\in [0,1)\), is denoted by \(x_{\varphi}\).
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On a System of Difference Equations [PDF]
Discrete Dynamics in Nature and Society, 2013 We have investigated the periodical solutions of the system of rational difference equations , and where .
Abdullah Selçuk Kurbanli, Ozan Özkan
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