Periodic Solutions To Josephson-type Systems

Hamiltonian system is one of the most fundamental research fields in differential systems. One of its primary aim is to investigate the existence and numbers of periodic solutions of differential systems with nonlinearities satisfying various conditions. The basic principles and methods it uses include topological degree theory, variational method and so on. By use one of the basic and widely applicable methods of the two above-variational method, we study the existence of (multiple) solutions of differential systems of Josephson-type with unbounded or periodic nonlinearities.The main results obtained in this thesis can be summarized as follows:1. In the introduction, we give backgrounds and applications of Josephson-type system as well as the current situation in the field. And at last, we bring forward what we investigate in this paper.2. In chapter 2, we introduce some preliminaries related to this paper in order to give a theoretical basis to study Josephson-type system.3. Chapter 3 is the main part of this pape, where we study the existence of (multiple) solutions of Josephson-type system with unbounded or periodic nonlinearities. Some new results are obtained and some results in the literature are improved.