Solvability and iterative algorithms for a higher order nonlinear neutral delay differential equation

The paper is concerned with the higher order nonlinear neutral delay differential equationr(t)(x(t)+p(t)x(t-τ))(m)(n-m)+(-1)n-m+1ft,xσ1(t),…,x(σl(t))=g(t),t⩾t0.Using the Banach fixed-point theorem, we establish five existence results of uncountably many bounded nonoscillatory solutions for the above equation, construct five Mann iterative sequences with mixed errors for approximating these nonoscillatory solutions and discuss five error estimates between the approximate solutions and these nonoscillatory solutions. To dwell the importance and applications of our results, five nontrivial examples are constructed.