Existence And Multiplicity Of Periodic Solutions And Homoclinic Solutions For Two Class Of Difference Systems With??₁,?₂?-Laplacian

In this dissertation,by using the least action principle and Clark theorem in the crit-ical point theory,the existence and multiplicity of periodic solutions and homoclinic so-lutions for a class of difference systems with classical(?1,?2)-Laplacian are considered.This dissertation is composed of four chapters.The content of the dissertation is as fol-lows.In the first Chapter,a brief introduction is given to the background for the investigat-ed problems,research status and some preliminaries.In the second Chapter,the existence of periodic solutions for a class of difference systems with a(?1,?2)-Laplacian is considered:(?)By using the least action principle and definition of N-function and its properties,some existence criteria of periodic solutions are obtained under the condition that nonlinear ter-m has subconvex growth,(p,g)-sublinear growth and p-sublinear growth.Some examples are given to illustrate our results.In the third Chapter,the existence and multiplicity of homoclinic solutions for a class of difference systems involving(?1,?2)-Laplacian and a parameter are investigated:(?)where F is not periodic in n and has(p,q)-sublinear growth or(p,q)-linear growth.At first,by using the least action principle,at least one homoclinic solution of the system is obtained,and then by using Clark theorem,at least m distinct pairs of homoclinic solutions of the system is obtained,where f1 = f2 ? 0.Some examples are given to illustrate our results.In the fourth Chapter,this main work in the full text is summarized,and the next plan of the research issues is prospected.