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Analytical Solution to a Third-Order Rational Difference Equation
The Scientific World Journal, 2023 Inspired by some open conjectures in a rational dynamical system by G. Ladas and Palladino, in this paper, we consider the problem of solving a third-order difference equation. We comment the conjecture by Ladas.
Alvaro H. Salas S. +2 more
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Third order non-linear difference equation with neutral term [PDF]
E3S Web of Conferences, 2023 This paper aims to investigate the oscillatory characteristics of a neutral third order nonlinear difference equation. Utilizing the comparison principle, we get some new standards that guarantee that any solution to the neutral difference equation ...
Kaleeswari S., Rangasri S.
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Oscillation theorems for third order nonlinear delay difference equations [PDF]
Mathematica Bohemica, 2019 Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form \Delta(a_n(\Delta(b_n(\Delta y_n)^{\alpha})))+q_nf(y_{\sigma(n)})=0 to have property ${(\rm A)}$ or to be oscillatory.
Kumar S. Vidhyaa +3 more
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On third-order linear difference equations involving quasi-differences [PDF]
Advances in Difference Equations, 2006 We study the third-order linear difference equation with quasi-differences and its adjoint equation. The main results of the paper describe relationships between the oscillatory and nonoscillatory solutions of both equations.
Došlá Zuzana, Kobza Aleš
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Stability of the third order rational difference equation
MANAS: Journal of Engineering, 2020 In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\]where the initial conditions are non zero real numbers and are ...
Mehmet Emre Erdoğan
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Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations [PDF]
Mathematica Bohemica, 2023 We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation D_3y(n)+f(n)y^\beta(\sigma(n))=0, where $D_3 y(n)=\Delta(b(n)\Delta(a(n)(\Delta y(n))^\alpha))$ is studied.
Govindasamy Ayyappan +3 more
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Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments [PDF]
Mathematica Bohemica, 2021 In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation \Delta^3(x_n+a_n x_{n-l} +b_n x_{n+m})+p_n x_{n-k} - q_n x_{n+r}=0,\quad n\geq n_0 ...
Srinivasan Selvarangam +3 more
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Explicit bounds for third-order difference equations [PDF]
The ANZIAM Journal, 2006 AbstractThis paper gives explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher-order equations. The results extend recent work of the authors for second-order equations.
Berenhaut, Kenneth S. +2 more
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On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation
Journal of Applied Mathematics, 2023 The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are ...
M. E. Erdogan
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Alexandria Engineering Journal, 2023 In this research paper, the third-order fractional partial differential equation (FPDE) in the sense of the Caputo fractional derivative and the Atangana-Baleanu Caputo (ABC) fractional derivative is investigated for the first time. The importance of the
Shorish Omer Abdulla +2 more
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