Research About Periodic Solutions To Second Order Josephson-type System With Unbounded Nonlinearities

The aim of this thesis is to study existence of periodic solutions of second order Josephson systems under suitable conditions by variational methods such as minimax principle,minimax methods, and the saddle point theorem.Chapter 1 is devoted to the evolution and development of variational methods, and the problems that will be studied are presented.In Chapter 2, we introduce some essential definitions and preliminary theorems related to this thesis and a way of reducing second order Hamiltion systems problems to find periodic solutions for functionals.In Chapter 3, we introduce some theorems of second order Hamiltonian systems with sublinear conditions, we systematically introduce some classical existence results obtained by the least action principle and the Saddle point theorem in variational methods. We obtain some results of Josephson-type system, and present some other theorems of periodic solutions under a kind of sublinear conditions and generalized Ahmad-Lazer-Paul conditions.