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

Abstract

In this paper, we present sufficient conditions for the third-order nonlinear advanced difference equations of the form Δ(a(n))Δ(b(n)Δy((n)))=p(n)f(y(σ(n)))\Delta \left( {a\left( n \right)} \right)\Delta \left( {b\left( n \right)\Delta y\left( {\left( n \right)} \right)} \right) = p\left( n \right)f\left( {y\left( {\sigma \left( n \right)} \right)} \right) 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.

Keywords

• third-order difference equation
• property b
• advanced argument
• semi-canonical
• 39a10