Existence Of Homoclinic Orbits For Superquadratic Hamiltonian Systems

For the first order Hamiltonian systems and the second order Hamiltonian systems where H、V satisfy the superquadratic condition:We use the variational principle, the critical point theory and approximation methods, to study the existence of homoclinic orbits of the system (HS1) and (HS2) which meet the conditions of superquadratic but does not meet the (AR) condition. This dissertation is divied into four chapters.The first chapter is the overview of the development and the present situation of the theory of the existence of the homoclinic orbits of the Hamilton system, and introduces our main workThe second chapter is the preliminary knowledge,introduced in work is needed in theconcepts, symbols and related lemma.The third chapter with the aid of the critical point theorem and approximation method is discussed for the existence of subharmonic solutions of homoclinic orbit for a class of first-order Hamiltonian system. And also is discussed for the existence of subharmonic solutions and homoclinic orbit for a class of first-order Hamiltonian system which meet the conditions of superquadratic but does not meet the (AR) condition.In the last chapter with the aid of the critical point theorem and approximation method is discussed for the existence of subharmonic solutions and homoclinic orbit for a class of second-order Hamiltonian system. And also is discussed for the existence of subharmonic solutions and homoclinic orbit for a class of second-order Hamiltonian system which meet the conditions of superquadratic but does not meet the (AR) condition.