The Study On The Existence And Multiplicity Of Solutions For Several Classes Of Fractional Hamiltonian Systems

In this thesis,we mainly study the existence and multiplicity of solutions for several classes of fractional Hamiltonian systems.The whole paper is divided into four chapters.In chapter 1,we introduce the origin and development of fractional differential equations and the existing results on the existence and multiplicity of solutions for fractional Hamiltonian systems via variational methods.Meanwhile,we enumerate the preliminary knowledge needed in our study and present the main results obtained in this paper.In chapter 2,we mainly study the existence of solutions for a class of fractional Hamiltonian systems with local superquadratic growth conditions.We prove that these systems possess at least one nontrivial solution under some mild conditions.In chapter 3,we mainly study the multiplicity of solutions for a class of locally defined fractional Hamiltonian systems near the origin.We prove that these systems possess infinitely many solutions near the origin under some relatively weak conditions.In chapter 4,we mainly study the existence of ground state solutions for a class of fractional Hamiltonian systems with parameter .We prove that these systems possess at least one ground state solution without the periodic assumption.