On Positive Solutions Of A Higher Order Nonlinear Neutral System Of Differential Equations

This paper consider the existence and multiplicity of higher order nonlinear neutralIn the first of this article, with the development of nonlinear differential equations, thispaper study the nonlinear neutral differential equations in the form of the above. Under certainconditions, the equations contain equation or equations of documents [1-20].The second part of this article describes the definitions, symbols and theorems.In the third part, based on several ranges of functionpi, this paper gets8theorems.These theorems mainly use the Leray-Schauder nonlinear alternative theorem, Banach fixedpoint theorem. In order to prove the existence of the theorems, this paper constructs differentfunctions, gets that these functions have fixed points, verifies that fixed points are solutionsfor the system of differential equations, and then proves that the higher order nonlinearneutral system of differential equations have uncountably many bounded positive solutions.The last part of the article structures8examples as the application of the theorems.Through careful calculation and analysis, this paper gets the conclusion of the theorems arepractical.