| This thesis of Master is composed of four chapters. We respectively discuss the oscillation of the following difference equations, periodic solution and bound oscillation:△Xn+pnXn-k=0. (1)xn=axn-1+(1-a)f(xn-k. (2)△u(xn-cnxn-m)=pnxn-k, u≥2 is even integer (3)In the first chapter, we introduce the practical background of problems and the researching results.In the second chapter, we investigated oscillation for equation (1), and obtained the sufficient condition of equation (1) which improve the result in related literature.In the third chapter, we obtain the existence of two periodic solutions of equation (2).In the fourth chapter, we investigated even order nonlinear neutral difference equation, and obtain some sufficient conditions which extended and improved the known results in related literature.
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