The Existence Of Solutions For Fractional Differential Equations With Nonhomogeneous Boundary Conditions

In this paper,we study the fractional differential equations.The paper includes three parts of contents,firstly,we study the existence and nonexistence of positive solutions for a class of fractional differential equations with nonhomogeneous boundary conditions;secondly,we study the existence of solution for a class of fractional differential equation with integral boundary value problem at resonance;finally,we study the eigenvalue for a class of p-Laplacian operator fractional differential equations involving the integral boundary condition.In this article,we use the upper and lower solution method,the fixed point index theorem,the fixed point theorem of cone expansion and compression,coincidence degree theory and so on to study related problems.The main work of this paper is divided into five parts.In Chapter 1,we introduce the research significance and status of fractional order differential equation,and give some achievements in the light of the content of my paper.In Chapter 2,some basic definitions and related properties of fractional differential and integral which are associated with the research content of the paper closely are introduced and the basic theorems which will be used in the following to study.In Chapter 3,we study the existence and nonexistence of positive solutions for a class of fractional differential equations with nonhomogeneous boundary conditions.At first,we establish the equivalent integral equations of the original differential equation through the transformation and get the Green function,moreover,we discuss the properties of the Green function;secondly,we get the existence theorem of positive solution by using upper and lower solutions method;finally,we study the existence and nonexistence of positive solution and multiplicity of solutions with the disturbance parameters which show the influence on the existence of positive solutions for boundary value problem under some sufficient conditions by Schauder fixed point theorem.In the end,we give relevant examples to illustrate our conclusions.In Chapter 4,we study the existence of solution for fractional differential equation with integral boundary value problem at resonance.By using coincidence degree theory,we obtain and prove the theorem about existence of solutions for the integral boundary value problem.In Chapter 5,we study the eigenvalue for a class of p-Laplacian fractional differential equations involving the integral boundary condition.By using the fixed point theorem of cone expansion and compression,we get the existence and nonexistence theorem of positive solution under the impact of the disturbance parameters.