On the global behavior of the higher order difference equations

Nonlinear difference equations of higher order are of paramount importance the applications of several mathematical models in biology, economics, genetics, sociology, psychology, and so forth. In the first section, general informations were given about the difference equations and a summary of literature on nonlinear difference equations was given. In the second section, general definitions and theorems about difference equations were given. In the third section, of the x_{n+1}=x_{n}x_{n-1}-1 difference equation, in the forth section of the x_{n+1}=x_{n-1}x_{n-2}-1 difference equation, in the fifth section of the x_{n+1}=x_{n}x_{n-2}-1 difference equation and in the last section of x_{n}=x_{n-l}x_{n-k}-1 difference equation are studied the behaviour of positive solutions of difference equations.