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Global stability of some classes of higher-order nonlinear difference equations. (English) Zbl 1194.39012

The author gives proofs of some known results on global stability of higher-order nonlinear difference equations

x n+1 -x n =-px n +f(n,x n-h 1 ,,x n-h r ),n=0,1,2,,

where h i N, i=1,,r, rN, p[0,1] and the function f satisfies inequalities

|f(n,y 0 ,,y r )| i=0 r q i |y i |

or

|f(n,y 0 ,,y r )|β i=0 r |y i | α i ,

i=0 r α i =1,α i >0,β<1.

MSC:
39A30Stability theory (difference equations)
39A10Additive difference equations
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