Global behavior of the nonlinear difference equation xn+1=f(xn−s,xn−t)
- Sun, Taixiang
- Xi, Hongjian
DOIAbstract
AbstractIn this note we consider a nonlinear difference equation of the form xn+1=f(xn−s,xn−t),n=0,1,…, under some certain assumptions, where s,t∈{0,1,2,…} with s<t and the initial values x−t,x−t+1,…,x0∈(0,+∞). We prove that the length of its finite semicycle is less than or equal to t and give sufficient conditions under which every positive solution of this equation converges to the positive equilibrium. Some known results are included and improved
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