Existence And Mann Iterative Algorithms Of Positive Solutions For Higher Order Nonlinear Differential Equation

This paper deals with the higher order nonlinear neutral delay differential equation where l,m,n≥1 are integers,piBased on the Banach fixed point theorem and new techniques, we prove the existence of uncountably many bounded positive solutions for the above equation, construct some Mann type iterative algorithms with errors to approximate these positive solutiens and discuss several error estimates between the sequences generated by the iterative algorithms and these positive solutions. Our results extend, improve and unify Cases (a) and (c) of Theorem 1, Cases (a) and (c) of Theorem 2 and Cases (a) and (c) of Theorem 3 in [1], Cases 1 and 3 of Theorem in [2], Theorems 2.2 and 3.2 in [3], Theorems 3.3 and 3.5 in [4], Theorem 2.1 in [5], Theorems 1 and 3 in [6], Theorems 1,2 and Corollary in [7]. Three examples are presented to illuminate the results obtained in this paper.