Invariants for some difference equations
A function \(I(x_{n-k},\dots, x_n)\) is called an invariant of the difference equation \(x_{n+1}= f(x_n,\dots,\) \(x_{n-k})\), if \(I\) is constant for every solution \(x_n\) and for all \(n\geq 0\). A positive solution is said to persist if it is bounded away from zero. For three types of nonlinear difference equations, invariants are constructed, and the invariants are used to see whether all solutions are bounded and persist. Analogous considerations are made for three systems of difference equations.
scientific article; zbMATH DE number 1053564