On the oscillation and periodic character of a third order rational difference equation

STUDYING THE BEHAVIOR OF SOLUTIONS OF A SECOND-ORDER RATIONAL DIFFERENCE EQUATION AND A RATIONAL SYSTEM

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.  

The Periodic Character of a Rational Difference Equation 3

with y−s, y−s+1, . . . , y−1 ∈ (0,∞) and k, m ∈ {1, 2, 3, 4, . . .}, where s = k+m. We prove that if gcd(2k,m) = 1, then solutions to this equation are asymptotically 2k-periodic. This generalizes the corresponding result for m = 3 and k = 1, proved in K. S. Berenhaut et al., Periodic Solutions of the Rational Difference Equation yn = yn−3+yn−4 yn−1 ,Journal of Difference Equations and Applicat...

studying the behavior of solutions of a second-order rational difference equation and a rational system

in this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.

On the Oscillation of Certain Third-order Difference Equations

(ii) {g(n)} is a nondecreasing sequence, and limn→∞ g(n)=∞; (iii) f ∈ (R,R), x f (x) > 0, and f ′(x)≥ 0 for x = 0; (iv) αi, i= 1,2, are quotients of positive odd integers. The domain (L3) of L3 is defined to be the set of all sequences {x(n)}, n ≥ n0 ≥ 0 such that {Ljx(n)}, 0≤ j ≤ 3 exist for n≥ n0. A nontrivial solution {x(n)} of (1.1;δ) is called nonoscillatory if it is either eventually posi...

On a Conjecture for a Higher-Order Rational Difference Equation