Homoclinic solutions for a higher order difference equation

2018 ◽  
Vol 86 ◽  
pp. 186-193 ◽  
Author(s):  
Lingju Kong
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Homoclinic Solutions ◽  
Order Difference ◽  
Order Difference Equation

scholarly journals Multiplicity of Periodic Solutions for a Higher Order Difference Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ronghui Hu
Keyword(s):  
Difference Equation ◽  
Periodic Solutions ◽  
Higher Order ◽  
Critical Groups ◽  
Order Difference ◽  
Reduction Methods ◽  
Order Difference Equation

We study a higher order difference equation. By Lyapunov-Schmidt reduction methods and computations of critical groups, we prove that the equation has fourM-periodic solutions.

Periodicity of the solution of a higher order difference equation

2018 ◽  
Author(s):  
A. M. Alotaibi ◽  
M. S. M. Noorani ◽  
M. A. El-Moneam
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Order Difference ◽  
Order Difference Equation

scholarly journals A Global Convergence Result for a Higher Order Difference Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
Bratislav D. Iricanin
Keyword(s):  
Global Convergence ◽  
Difference Equation ◽  
Bounded Solution ◽  
Convergence Result ◽  
Higher Order ◽  
Unbounded Solution ◽  
Order Difference ◽  
Initial Values ◽  
Order Difference Equation

Letf(z1,…,zk)∈C(Ik,I)be a given function, whereIis (bounded or unbounded) subinterval ofℝ, andk∈ℕ. Assume thatf(y1,y2,…,yk)≥f(y2,…,yk,y1)ify1≥max{y2,…,yk},f(y1,y2,…,yk)≤f(y2,…,yk,y1)ify1≤min{y2,…,yk}, andfis non- decreasing in the last variablezk. We then prove that every bounded solution of an autonomous difference equation of orderk, namely,xn=f(xn−1,…,xn−k),n=0,1,2,…,with initial valuesx−k,…,x−1∈I, is convergent, and every unbounded solution tends either to+∞or to−∞.

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