Several Types Of P-laplacian Multi-point Boundary Value Problems And Non-linear Differential Equations The Existence Of The Study

This dissertation deals with the existence of positive periodic solutions to one kind of nonlinear functional differential system with feedback control, as well as the existence and multiplicity of positive solutions to p - Laplacian multi-point boundary value problems. The methods and techniques employed here are involved in nonlinear functional analysis, such as Avery-Peterson fixed-point theorem,cone tensile and compression fixed-point theorem,Leggett-Williams fixed-point theorem and double-cone fixed-point theorem. This dissertation consists of three chapters.In Chapter 1, we introduce the background and research status on the nonlinear functional differential system with feedback control and p- Laplacian multi-point boundary value problems at home and abroad. We also present a brief survey of our results.In Chapter 2, by using Avery-Peterson fixed-point theorem, we investigate the existence of multiple positive periodic solutions to the nonlinear non-autonomous functional differential system with feedback control, and prove that this system admits at least three positive periodic solutions under certain growth conditions imposed on the nonlinearity.In Chapter 3 we investigate several kinds of p- Laplacian third-order three-point boundary value problems, we discuss the existence, multiplicity and no-existence of positive solution to these problems by using double-cone fixed-point theorem, Leggett-Williams fixed-point theorem and cone-tensile and cone-compression fixed-point theorem, separately.