Different techniques for studying oscillatory behavior of solution of differential equations

Abstract

The aim of this work is to study oscillatory behavior of solutions for a fourth-order neutral nonlinear differential equation ${\left(b\left(x\right){\left(w^{m-1}\left(x\right)\right)}^{\gamma }\right)}^{\prime }+{\sum }_{i=1}^j{q}_i\left(x\right)f\left(w\left(g_i\left(x\right)\right)\right)=0$, $x\ge x_0$. The results obtained are based on the Riccati transformation, integral averaging technique and the theory of comparison with second-order delay equations. The obtained results complements and generalize the earlier ones. Some examples are illustrated to show the applicability of the obtained results.