| In this paper, the dynamics, i.e., the global stability, the period character and the bound-edness nature of the solutions of several classes of difference equations, are studied, which answer some open problems and generalize some known results. This paper is composed of five chapters.In chapter one, the historic background of the difference equations is introduced briefly.In chapter two, some basic definitions and known results for the difference equations are introduced.In chapter three, we study the dynamics of the difference equationwhere pn > 0 is a period-k sequence, s∈{1,2,...}, and the initial conditions x-3s+1, x-3x+2,..., x0∈(0, +∞), and obtain the following results:(1) If gcd(3s, k) - 1, then every positive solution of this equation is bounded.(2) If s = 1, k = 2 and p1 > p0 > 1, then the unique prime period-2 solution of this equation is globally asymptotically stable.In chapter four, we study the dynamics of the difference equationwhere Bn > 0 is a bounded sequence and the initial conditions x-1, x0∈(0, +∞), and obtain the following results:(1) If Bn is a period-p sequence, p (?) 3s (s∈N) and (?)Bi > 1,then every positive solution of that equation is bounded.(2) If Bn is an increasing sequence, then every positive solution of that equation is bounded.(3) If Bn is a period-2 sequence, then the unique prime period-2 solution of that equation is globally asymptotically stable. In chapter five, we study the boundedness of the difference equationwhereβn > 0 is a period-2 sequence withβ0 <β1, A∈(0, +∞) and the initial conditions x-2, x-1, x0∈(0,+∞). We show that if 1 - A (?) [β0,β1], then every positive solution of that equation is bounded.
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