Results 1 to 10 of about 1,801,571 (229)
On the oscillation of third order half-linear neutral type difference equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2011 In this paper, the authors study the oscillatory properties of third order quasilinear neutral difference equation of the form $$\Delta(a_{n}(\Delta^{2}(x_{n} + p_{n}x_{n-\delta}))^{\alpha}) + q_{n} {x^{\alpha}_{n-\tau}} = 0,\quad n\geq 0, \tag{E ...
Ethiraju Thandapani +2 more
doaj +4 more sources
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
doaj +7 more sources
Oscillation of certain third-order difference equations [PDF]
Computers & Mathematics with Applications, 2001 New criteria for oscillatory behavior of all solutions of third-order difference equations of the type \[ \Delta^3 x_n=p_n \Delta^2x_{n+m} +q_n F(x_{n-g}, \Delta x_{n-h}) \] are presented.
Ravi P. Agarwal, Said R. Grace
openalex +3 more sources
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
doaj +3 more sources
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
doaj +3 more sources
Dynamics of a system of rational third-order difference equation [PDF]
Advances in Difference Equations, 2012 In this paper, we study the dynamical behavior of positive solution for a system of a rational third-order difference ...
Qianhong Zhang +2 more
openalex +4 more sources
Basins of Attraction for Third-Order Sigmoid Beverton Holt Difference Equation [PDF]
MathematicsThe third-order difference equation yn+1=a1yn21+yn2+a2yn−121+yn−12+a3yn−221+yn−22, as a potential discrete time model of population dynamics with three generation involved, is studied.
Mustafa R. S. Kulenović, Ryan Sullivan
doaj +2 more sources
On a Third‐Order System of Difference Equations with Variable Coefficients [PDF]
Abstract and Applied Analysis, 2012 We show that the system of three difference equations , , and , n ∈ ℕ0, where all elements of the sequences , , , n ∈ ℕ0, i ∈ {1,2, 3}, and initial values x−j, y−j, z−j, j ∈ {0,1, 2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when ...
Stevo Stević +3 more
openalex +5 more sources
Oscillation of third-order nonlinear delay difference equations
Turkish Journal of Mathematics, 2012 Third-order nonlinear difference equations of the form Δ(cnΔ(dnΔxn)) + pnΔxn+1 + qnf (xn−σ )= 0 ,n ≥ n0 are considered. Here, {cn} , {dn} , {pn} ,a nd{qn} are sequences of positive real numbers for n0 ∈ N, f is a continuous function such that f (u) /u ≥ K> 0f oru 0 .
Mustafa Fahri Aktaş +2 more
openalex +5 more sources
Neimark-Sacker Bifurcation of a Third Order Difference Equation
Fundamental Journal of Mathematics and Applications, 2019 In this paper, we investigate the bifurcation of a third order rational difference equation. Firstly, we show that the equation undergoes a Neimark-Sacker bifurcation when the parameter reaches a critical value. Then, we consider the direction of the Neimark-Sacker bifurcation. Finally, we give some numerical simulations of our results.
Marwan Aloqeili, Asmaa SHAREEF
openalex +5 more sources