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This talk is concerned with the oscillatory behavior of difference equations correspondingto the second-order nonlinear differential equation x″+ f(x)=t2 =0,where f is continuous on R and satisfies xf(x) ＞ 0 if x≠0.Obtained results are represented as a pair of oscillation theorem and non-oscillation theorem.These results are best possible in a certain sense.A discrete version of the Riemann-Weber generalization of the Euler differential equation and its extended equations play an important role to prove our results.The proofs of our results are based on Riccati technique and phase plane analysis of a system.