On the asymptotic properties of continuous solutions of the systems of nonlinear functional equations (Q384043)

Let \(q>0,q\neq 1\) be fixed, let further \(F:\mathbb R_+\times\mathbb R^n\times\mathbb R^n\to\mathbb R^n\) and \(f:\mathbb R_+\to\mathbb R_+\) be known functions, and consider the functional equation \[ x(qt)=x(t)+F\bigl(t,x(t),x(f(t))\bigr). \] The Author gives conditions for the involved known functions under which a certain kind of asymptotic equilibrium of the system above can be guaranteed.