The Existence Of Positive Solutions To Nonlinear Boundary Value Problem With P-Laplacian Operator

This paper mainly study the existence and multiplicity of positive solutions to the fourth-order nonlinear boundary value problem with p-Laplacian operator and the multipoint one-dimensional p-Laplacian boundary value problems with impulsive effeets.This paper consists of three chapters:In Chapter 1,we introdnced the historical background and the main works of this paper,and we outlined some basie knowledges.In Chapter 2,we study the existence and multiplicity of positive solutions to the fourth-order nonliinear boundary value problem with p-Laplacian operator.Firstly,we provide sufficient conditions for the existence of positive solutions for the boundary value problem by the fixed point theorem,when the nonlinear term is continuous;Secondly,we show that it.has at least one or two positive solutions by applying the fixed point theorem,when the nonlinear term may change sign;Lastly.we obtain the existence of one positive solutions and multiple positive solutions for nonlinear singular boundary value problem when the nonlinear term is a lower semi-continuous function,by using the linear approaching method and the Fatou Lemma,Lebesgue dominated convergence theorem.In Chapter 3,we provide sufficient conditions for the existence of multiple positive solutions to the multipoint boundary value problem by the fixed-point theorem of Leggett-Williams.