Periodic Solutions Of Delay Difference Equations

The existence and multiplicity of periodic solutions for nonlinear delay difference equations is an important research direction of delay difference equation,and it has important theoretical significance and physical background. Using critical point theory, we consider the existence and multiplicity of nontrivial periodic solutions for two types of first order suplinear delay difference equations in this paper.This paper consists of three chapters as follows:In chapter one, we introduce the historical background, the research status,the main work and relevant preparation knowledge.In the second chapter, we consider a class of first-order delay difference equations. By establishing suitable variational framework, we turn the periodic solution problem to the critical point problem of corresponding functional. Using Linking Theorem, we obtain some suffcient conditions on the existence and multiplicity of periodic solutions for delay difference equations. Our results extend and improve some existed results.In the third chapter, we consider a class of first-order delay difference equations (?).When f(u) grows suplinearly both at zero and infinity, several results obtained for the existence and multiplicity of periodic solutions to delay difference equations by making use of Linking Theorem.