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

In this paper,we mainly study the existence and multiplicity of solutions of several kinds of fractional differential equations with p-Laplacian operator.We improve and generalize the results of some existing literatures.The full paper is divided into four chapters:Chapter 1 briefly introduces the research background,current research situation and main work of this paper,and briefly introduces some basic definitions,theorems and properties of fractional calculus.In chapter 2,we study the existence of positive solutions for a class of nonlinear fractional differential equations with p-Laplacian operator.We use Guo-Krasnosel'sKii fixed point theorem to obtain the existence result of the solution of the differential equation.Chapter 3 is about a class of integro-boundary value problems.First,the system is transformed into an equivalent integral equation,and then the sufficient conditions for the existence and uniqueness of the boundary value problem are obtained by using the Banach contraction mapping principle.On this basis,we also consider a three-point boundary value problems on infinite interval.According to the method of judging the relative compactness on the infinite interval,and combining with Schauder fixed point theorem,the existence result of the solution of the three-point boundary value problem is obtained.Chapter 4 considers a class of m point boundary value problems.The integral equation equivalent to the m point boundary value problem is given first,and then the existence and multiplicity of positive solutions of the m point boundary value problem are given by studying the properties of Green function and combining with the Guo-Krasnosel'skii fixed point theorem.