Nonoscillatory Solutions for Higher-Order Neutral Dynamic Equations on Time Scales

Abstract

We study the higher-order neutral dynamic equation ${\left\{a\left(t\right){\left[{\left(x\left(t\right)-p\left(t\right)x\left(\tau \left(t\right)\right)\right)}^{{\Delta }^m}\right]}^{\alpha }\right\}}^{\Delta }+f\left(t,x\left(\delta \left(t\right)\right)\right)=0$ for $t\in {\left[t_0,\infty \right)}_{\mathbb{T}}$ and obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.