On the behaviour of solutions of a class of difference equations involving generalized difference operator

In this master's thesis, some new results are given for nonoscillation and oscillation of all solutions of higher-order difference equation involving generalized difference operator of the form ∆_a^k (p_n ∆_a^2 y_n )=f(n,y_n,∆_a y_n,∆_a^2 y_n,…,∆_a^(k+1) y_n) where n∈N, a∈R-{0}, k≥1 and {p_n} is real sequence with p_n≠0 for n∈N and f:N×R^(k+2)→R. This thesis has three parts. The first part consists of the preamble. In the second part, basic definitions and theorems for difference equations are reminded and finally, in the third part, some results and examples are given for nonoscillation and oscillation of all solutions of the above difference equation.