Global behaviour of solutions of the rational difference equation with variable coefficient

Difference equations are applied into mathematical models covering biology, genetics, population dynamics, probability theory, psychology, sociology and many scientific disciplines. That is why, in recent years, there is great interest on the difference equation. In this thesis, some known results about difference equation in the literature are shown. This study consists of five chapters. In the first chapter, general information about difference equation and the literature summary of researches on non-linear rational difference equation are given. In the second chapter, general definition and theorem concerning difference equation is given. In the third chapter, the behaviour of positive solutions firstly of the equation〖 x〗_(n+1)=α+x_(n-1)/x_n and then of the equation 〖 x〗_(n+1)= α_n+x_(n-1)/x_n in the case when {α_n } which is convergent or the period-two sequence are examined. In this chapter, finally, the behaviour of positive solutions of the difference equation〖 x〗_(n+1)= p_n+x_(n-1)/x_n in the case when {p_n } which is positive bounded sequence are dealt with. In the fourth chapter, findings and discussion sections and finally in the fifth chapter conclusion is included. KEYWORDS: Attractivity, equilibrium point, sequence, difference equation, stability, periodicity, period, the oscillatory, boundedness.