Existence Of Nonoscillatory Solutions For A Third-order Nonlinear Neutral Delay Differential Equation

This paper is to investigate the solvability of a third-order nonlinear neutral delaydifferential equation of the formThis paper shows the existence of uncountably many bounded nonoscillatory solutionsfor the above differential equation under seven cases below by using Krasnoselskii’s fixedpoint theorem and Schauder’s fixed point theorem:The seven cases discussed above make this paper more comprehensive, also extend andcomplement the results of many previous which we will mention below. When the nonlinearfunctions term turns to a linear function, or[(t)(g (t, x (g1(t)),, x (g n(t)))]=0、q (t)0, h (t, x (h1(t)),, x (h n (t))0,t t0,the above equation can contain the equationsenumerated in the article, which means the equation of this form is more general. Seven non-trivial examples are given in the last to illustrate the superiority of the results in thispaper.