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.