A higher order nonlinear neutral differential equation

Abstract

This paper is concerned with the higher order nonlinear neutral differential equationBy dint of the Leray-Schauder nonlinear alternative, Rothe fixed point theorem and some new techniques, we prove the existence of uncountably many bounded positive solutions for the equation. Several nontrivial examples are given to illustrate the applications and advantages of the results presented in this paper. Keywords:Higher order nonlinear neutral differential equation, uncountably many bounded positive solutions, Leray-Schauder nonlinear alternative theorem, Rothe fixed point theorem.