Oscillation and nonoscillation of nonlinear second order difference equations

In this paper, we study oscillation and nonoscillation behaviour of the second order nonlinear difference equations of the form $$\Delta (r_n \psi (x_n )\Delta x_n ) + q_{n + 1} f(x_{n + 1} ) = 0, n \in N(n_o ),$$ and $$\Delta (r_n \psi (x_n )\Delta x_n ) + q_n f(n,x_n ) = 0, n \in N(n_o ),$$ whereN(n _o ) =n _o ,n _o + 1, …, (n _o is a fixed nonnegative integer number), Δx_n =x _n +1?x _n is the forward difference operator,x :N(n _o ) → ?,r :N(n _o ) → (0, ∞), Ψ : ? → (0, ∞),f is a real valued continuous function, andq _n is a sequence of real valued.