Oscillation and asymptotic behavior of third-order semi-canonical difference equations with positive and negative terms

This paper deals with the oscillatory and asymptotic properties of third-order semi-canonical difference equations with positive and negative terms of the form\Delta\left(\varphi(\ell)\Delta\left(\psi(\ell)\Delta \mu(\ell) \right) \right)+\xi(\ell)f(\mu(\sigma(\ell)))-\chi(\ell)g(\mu(\tau(\ell)))=۰.Using a canonical transformation technique, we offer new criteria which imply that the solutions of the studied equation are almost oscillatory. Some examples are provided to support our results.

کلیدواژه ها:

Third-order ، semi-canonical ، difference equation ، oscillation ، positive and negative term