scholarly journals Unbounded positive solutions of higher-order difference equations with singular nonlinear term

2000 ◽  
Vol 39 (3-4) ◽  
pp. 177-184 ◽  
Author(s):  
Wan-Tong Li ◽  
Xian-Ling Fan ◽  
Cheng-Kui Zhong
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
Nonlinear Term ◽  
Higher Order ◽  
Order Difference

scholarly journals Global Behavior of Two Families of Nonlinear Symmetric Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Wanping Liu ◽  
Xiaofan Yang ◽  
Luxing Yang
Keyword(s):  
Asymptotic Stability ◽  
Recent Result ◽  
Positive Solutions ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Exponential Convergence ◽  
Higher Order ◽  
The Other ◽  
Global Behavior ◽  
Order Difference

We mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in Stević's paper (2010). A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of Aloqeili (2009), Berenhaut and Stević (2007), and Liao et al. (2009).

scholarly journals Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Chengjun Yuan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Order Difference ◽  
Existence Of Positive Solutions

This paper studies the boundary value problems for the fourth-order nonlinear singular difference equationsΔ4u(i−2)=λα(i)f(i,u(i)),i∈[2,T+2],u(0)=u(1)=0,u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone.

scholarly journals Dynamics of a Class of Higher Order Difference Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-6
Author(s):  
Bratislav D. Iricanin
Keyword(s):  
Continuous Function ◽  
Difference Equation ◽  
Positive Solutions ◽  
Difference Equations ◽  
Higher Order ◽  
Positive Equilibrium ◽  
Order Difference

We prove that all positive solutions of the autonomous difference equationxn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, wherek,m∈ℕ, andfis a continuous function satisfying the conditionβ min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um}for someβ∈(0,1), converge to the positive equilibriumx¯=(α−1)/(β+1)ifα>1.

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