Oscillation and Property B for Semi-Canonical Third-Order Advanced Difference Equations

In this paper, we present sufficient conditions for the third-order nonlinear advanced difference equations of the form Δ ( a ( n ) ) Δ ( b ( n ) Δ y ( ( n ) ) ) = p ( n ) f ( y ( σ ( n ) ) ) Δ ( {a( n )} )Δ ( {b( n )Δ y( {( n )} )} ) = p( n )f( {y( {σ ( n )} )} ) to have property B or to be oscillatory. These conditions are based on monotonic properties and estimates of nonoscillatory solutions of corresponding canonical type equations. The obtained results extended and improve known results mentioned in the literature.