Existence Of Periodic Solutions For A Class Of Discrete Systems With??₁,?₂?-Laplacian

With the rapid development of electronic computing technology,nonlinear differ-ence equation theory has become one of the important theoretical basis in real life.The study on existence and related properties of difference system has important theoretical and practical significance,and become an important topic of many scholars.In this paper,by using the saddle point theorem and the least action principle,we investigate the existence of periodic solutions for the follow(?1,?2)-Laplace discrete system:(?)These results generalize some results of the known literature.This dissertation consists of four chapters.In the first chapter,we introduce the background and significance of the topic,and introduce the variational principle,research status and preliminary knowledge briefly.In the second chapter,the corresponding variational structure is introduced and the relevant lemma is given.In the third chapter,we study the existence of periodic solutions of(?1,?2)-Laplace system under the non-autonomous case.Based on the variational framework and related lemmas in chapter second,when the nonlinear term F(t,.,.)satisfies(p,q)growth conditions,by using saddle point theorem,we study the existence of periodic solutions of systems from the classic homeomorphism and bounded homeomorphism,and obtain some new existence results.Finally,we give some examples to illustrate the feasibility of the obtained results.In the fourth chapter,we study the existence of periodic solutions of(?1,?2)-Laplace system under the autonomous case with perturbed term.When the nonlinear term satisfies similar Lipschitz growth,by using the least action principle,we study the existence of periodic solutions of systems from the classic homeomorphism and bounded homeomorphism,and obtain some new existence results.Finally,we give some examples to illustrate the feasibility of the obtained results.In the fifth chapter,we make a brief summary of the full text and review,and make a prospect for the next step of the research issues.