We show that the equation in the title with nonnegative parameters and nonnegative initial conditions exhibits a trichotomy character concerning periodicity, convergence, and boundedness which depends on whether the parameter n is equal, less, or greater than the sum of the parameters g and A .

Abstract We investigate the periodic character and the global stability of solutions of the equation y n  + 1  = ( p  +  y n  + 1 )/( qy n  +  y n  − 1 ) with positive parameters and positive initial conditions.

In this paper we give a necessary and sufficient condition for the oscillation of the second order linear differential equation where p is a locally integrable function and either or where We give some applications which show how these results unify and imply some classical results in oscillation theory.

We investigate the global stability, and the periodicity of the recursive sequence where the parameters α,β and A and the initial condition x-1 and Xo are non negative real numbers.