Oscillation Theorems for Second-Order Forced Neutral Nonlinear Differential Equations with Delayed Argument

Abstract

We are concerned with the oscillation of the forced second-order neutral nonlinear differential equations with delayed argument in the form ${\left(r\left(t\right){\left(x\left(t\right)+a\left(t\right)x\left(\sigma \left(t\right)\right)\right)}^{\prime }\right)}^{\prime }+p\left(t\right)f\left(x\left(\tau \left(t\right)\right)\right)+{\sum }_{i=1}^n{q}_i\left(t\right){\left|x\left(t\right)\right|}^{{\lambda }_i}\text{s}\text{n}\text{g}x\left(t\right)=e\left(t\right)$. No restriction is imposed on the potentials $p\left(t\right)$, $q_i\left(t\right)$, and$e\left(t\right)$ to be nonnegative. Our methodology is somewhat different from those of previous authors.