Existence Of Solutions For Boundary Value Problems Of Fractional Differential Equations With P-Laplacian

The theory of differential equations is an important part of mathematics.Many physical problems can be attributed to the models of differential equation.So the differential equation is the link of mathematics and physical problems.Boundary value problems of differential equations is a basic problem in the study of differential equations.With the emergence of new problems,Many new research direction come out.Fractional differential equations are important generalization of ordinary differential equations.Especially in recent decades,fractional differential equations have been widely applied in different areas including physi-cal,chemical,biological,mechanical.The boundary value problem of fractional differential equation with p-Laplacian operator has attracted extensive attention of scholars world wide and gradually becomes a hot topic.The present paper is devoted to the study of the existence of the boundary value problem of fractional differential equation with p-Laplacian,which includes the nonlinear differential equation,fractional impulsive differential equation,fractional delay differential equation and other circumstances.We study the existence and multiplicity of positive solution and give some new results.It is organized as follows:In Chapter 1,we introduce research background and present situation of fractional calculus,present situation and significance of research of the existence of solution for the boundary value problem of fractional differential equation with p-Laplacian operator and list some basic conceptions,as well as our main research work.In Chapter 2,we investigate the existence of resonance multi-point boundary value prob-lem of nonlinear fractional differential equation with p-Laplacian operator.By using Mawhin continuity theorem,some sufficient conditions of the existence of solution are obtained.In Chapter 3,we discuss the existence of four-point boundary value problem of p-Laplacian operator fractional differential equation with impulse.By using upper and lower solutions method and monotone iterative techniques,some sufficient conditions of the exis-tence of at least one solution arc obtained.In Chapter 4,we consider the existence of multiple positive solutions of the boundary value problem of p-Laplacian operator fractional differential equation with delay.By using Avery-Perterson fixed point theorem,Some sufficient conditions of at least three positive solutions are obtained,when the nonlinear term f satisfies a certain growth condition.