The Study On The Solutions Of Several Classes Of Fractional Boundary Value Problems

In this thesis,we mainly study the existence and multiplicity of solutions for several classes of fractional boundary value problems.The article divided into five chapters.In chapter one,we introduces the research background of fractional bound-ary value problems and the existing results in related literatures,which lead to the problems we will study in this paper.Meanwhile,we also give some related prelimilaries knowledge.In chapter two,we study the multiplicity of the solutions for the following fractional boundary value problems:We prove that it possesses infinitely many solutions under the superquadratic conditions:(?) uniformly for t ∈[0,T].In chapter three,we study the existence of the solutions for the following fractional boundary value problems:We prove that it possesses at least one nontrivial solution under the superquadratic condition:(?)uniformly for t∈[0,T].In chapter four,we study the multiplicity of the solutions for the fractional boundary value problems consider in chapter three.In the case where the nonlin-ear term W(t,u)is only defined near the origin with respect to u,we prove that it possesses a sequence of solutions concentrating near the origin.In chapter five,we study the existence of the solutions for class of fractional differential equations with parameter λ.We prove that it possesses at least one nontrivial solution for any λ>0 under some mild conditions.