scholarly journals On a Higher-Order Nonlinear Difference Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Bratislav D. Iričanin
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Higher Order ◽  
Nonlinear Difference Equation

This paper shows that all positive solutions of a higher-order nonlinear difference equation are bounded, extending some recent results in the literature.

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 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 for singular discrete boundary value problems

2004 ◽  
Vol 2004 (4) ◽  
pp. 271-283 ◽  
Author(s):  
Mariella Cecchi ◽  
Zuzana Došlá ◽  
Mauro Marini
Keyword(s):  
Continuous Function ◽  
Difference Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Nonlinear Difference Equation ◽  
Real Sequence ◽  
Positive Continuous Function ◽  
Positive Real ◽  
Singular Nonlinearities

We study the existence of zero-convergent solutions for the second-order nonlinear difference equationΔ(anΦp(Δxn))=g(n,xn+1), whereΦp(u)=|u|p−2u,p>1,{an}is a positive real sequence forn≥1, andgis a positive continuous function onℕ×(0,u0),0<u0≤∞. The effects of singular nonlinearities and of the forcing term are treated as well.

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