Introduction

In this book we are interested in the global character of solutions of the thirdorder rational difference equation

xn+1 = α+ βxn + γxn−1 + δxn−2 A+Bxn + Cxn−1 +Dxn−2

, n = 0, 1, . . . , (0.0.1)

where the parameters α, β, γ, δ,A,B,C,D are nonnegative real numbers and the initial conditions x−2, x−1, x0 are arbitrary nonnegative real numbers such that the denominator is always positive.