n-th order essential nonlinear difference equations with Property A or B

Consider difference equation ∆^((n) ) u(k)+F(u)(k)=0, where ∆^((n) ) u(k) is n-th order difference operator. F:S(N,R)→S(N,R) (S(N,R) denote the set of discrete functions whose set of values is R). Sufficient conditions for the above equation to have Property A and B are established, when operator F has a nonlinear minorant different from Emden-Fowler type nonlinear minorant.

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