Existence of monotone solutions of a difference equation
Summary: We consider the nonlinear difference equation \(x_{n+1}=f(x_{n - k},x_{n - k+1},\dots ,x_{n}), n=0,1,\dots ,\) where \(k\in {1,2,\dots }\) and the initial values \(x_{ - k},x_{ - k+1},\dots ,x_{0}\in (0,+\infty )\). We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this way some results of the literature.
scientific article; zbMATH DE number 5538674
scientific article