Monotonicity of Eventually Positive Solutions for a Second Order Nonlinear Difference Equation

2010 ◽  
Author(s):  
Chen Huiqin ◽  
Jin Zhen
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Second Order ◽  
Nonlinear Difference Equation

scholarly journals Monotonicity of Eventually Positive Solutions for a Second Order Nonlinear Difference Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Huiqin Chen ◽  
Zhen Jin ◽  
Shugui Kang
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Monotone Solutions

We derive several sufficient conditions for monotonicity of eventually positive solutions on a class of second order perturbed nonlinear difference equation. Furthermore, we obtain a few nonexistence criteria for eventually positive monotone solutions of this equation. Examples are provided to illustrate our main results.

scholarly journals Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-21
Author(s):  
Zeqing Liu ◽  
Xin Li ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Difference Equation ◽  
Iterative Method ◽  
Positive Solutions ◽  
Iterative Algorithms ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Banach Fixed Point Theorem ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Delay Difference

This paper deals with the second-order nonlinear neutral delay difference equationΔ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn,n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field.

scholarly journals Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Xiu-Mei Jia ◽  
Wan-Tong Li
Keyword(s):  
Difference Equation ◽  
Global Attractor ◽  
Positive Solutions ◽  
Local Stability ◽  
Global Attractivity ◽  
Initial Conditions ◽  
Higher Order ◽  
Nonlinear Difference Equation ◽  
Positive Equilibrium ◽  
Prime Period

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: , , where the parameters and the initial conditions . We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.

scholarly journals Asymptotic Behavior of a Second-Order Fuzzy Rational Difference Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Q. Din
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Second Order ◽  
Qualitative Behavior ◽  
Existence Of Positive Solutions ◽  
Rational Difference Equation ◽  
Boundedness And Persistence ◽  
Theoretical Results

We study the qualitative behavior of the positive solutions of a second-order rational fuzzy difference equation with initial conditions being positive fuzzy numbers, and parameters are positive fuzzy numbers. More precisely, we investigate existence of positive solutions, boundedness and persistence, and stability analysis of a second-order fuzzy rational difference equation. Some numerical examples are given to verify our theoretical results.

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