Multiplicity Of Periodic Solutions For A Class Of Discrete （φ₁,φ₂）-Laplacian Systems

With the development of computers, the difference system plays a very important role in our life and production. So the research on difference system has important theoretical significance and practical value. The study on existence and multiplicity of periodic solutions for difference systems has always been a classical topic, and many scholars have made lots of contributions. Recent years, variational method has become an important method to solve such problems. The main idea of variational method is that one can seek critical points of the corresponding variational functional if one wants to seek solutions of systems.In this dissertation, we apply the minimax principle to study the existence and multiplicity of periodic solutions for the following nonlinear difference dynamic sys-tem:This dissertation consists of four chapters. In the first chapter, we mainly introduce the background and significance of this topic that we investigated, and introduce briefly the variational method used in this dissertation and current status of this topic. In the second chapter, we construct variational structure of nonlinear (φ1,φ2)-Laplacian dif-ferential dynamical system studied in this dissertation. In the third chapter, under sub-(q,p) growth conditions, we study the existence and multiplicity of solutions of sys-tem from the following two aspects:classical homeomorphism mapping and bounded homeomorphism mapping, respectively. By using some abstract critical point theorems and research techniques, we obtain some new multiplicity results. These results extend and improve some known results. In the fourth chapter, we summarize the main work in this dissertation and make a prospect for our future research direction.