LAUSR

In this paper, we establish the qualitative behavior of the even-order advanced differential equation ${\left(a\left(\upsilon \right){\left(y^{\left(\kappa -1\right)}\left(\upsilon \right)\right)}^{\beta }\right)}^{\prime }+{\displaystyle {\sum }_{i=1}^j{q}_i}\left(\upsilon \right)g\left(y\left({\eta }_i\left(\upsilon \right)\right)\right)=0,\upsilon \ge {\upsilon }_0$ . The results obtained are based on the Riccati transformation and the theory of comparison with first- and second-order equations. This new theorem complements and improves a number of results reported in the literature. Two examples are presented to demonstrate the main results.