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One case of appearance of positive solutions of delayed discrete equations. (English) Zbl 1099.39001
The authors study the existence of a positive solution of the nonlinear delay discrete equation \[ \Delta u(k+n)=f\big (k,u(k),u(k+1),\dots ,u(k+n)\big ), \quad k\in {\mathbb Z},\;k\geq a. \] They derive a sharp sufficient condition for the existence of such solution. The result is a special case with \(b(k)\equiv 0\) and \(c(k):=\sqrt {k}\, \big ( \frac {n}{n+1} \big )^k\) of the existence and boundedness result.

MSC:
39A10 Additive difference equations
39A11 Stability of difference equations (MSC2000)
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