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Sufficient conditions for the global stability of nonautonomous higher order difference equations. (English) Zbl 1078.39005

The authors consider some problems of stability and qualitative behavior for difference equations of the form \[ x_{n+1} = f(n,x_n,\ldots,x_{n-T}), \] the linear equation \[ x_{n+1} - x_n = -\sum_0^N a_k(n)x_{n-k} \] and the equation \[ x_{n+1} - x_n = -\sum_0^N a_k(n)x_{n-k} + f(n,x_n,\ldots,x_{n-T}) \] Results on exponential stability and stability by the first approximation are presented. An application from macroeconomics is given.

MSC:

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
91B64 Macroeconomic theory (monetary models, models of taxation)
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