Existence And Multiplicity Of Solutions For Some Kinds Of Fractional Differential System

In this paper,we mainly investigates the existence and the multiplicity of solutions for some kinds of fractional differential system by using the critical point theory.There are five chapters and the main contents are as follows:At the beginning,the first chapter describes the background and significance of investigating problems,and reviews the history and recent advancement of fractional differential equations.Then,in the second chapter,some preliminaries of fractional differential equations and knowledge about the critical point theory are given.In the third chapter,we use the least action principle and the saddle point theorem to study the existence of solutions for the following a class of fractional boundary value problem Specifically,this chapter contains two main parts.In the first part,we introduce control functions h(t)and h*(t),and mainly focus on the existence of solutions for fractional boundary value problem in the case that the nonlinear term is sublinear.In the second part,we introduce two kinds of control functions ?(t)and ?*(t),and study the existence of solutions for the above problem when the nonlinearity does not increase more than |x| at infinity.In the fourth chapter,by using the mountain pass lemma and Ekeland variation method,we study and obtain the existence and multiplicity of solutions for the following nonhomogeneous fractional boundary value problem has at least two nontrivial solutions.Finally,in the fifth chapter,we study the existence of solutions for the following fractional boundary value problem by applying the mountain pass lemma and Ekeland variation method,where W(t,x)= AG(t,x)+ F(t,x),?>0,F(t,x)is superquadratic and G(t,x)is subquadratic at infinity.