Research On Oscillatory Properties For Some Classes Of Partial Difference Equations

This dissertation consists of five chapters.Its concern concentrates on the oscillatory property of some classes of partial difference equations by means of the envelope theory.The first chapter is preface,in which the studying background,theoretical frame of this thesis are exhibited.In the second chapter,we study the oscillatory property for the partial difference equation pum+2,n +qum,n+2 + um+1,n + um,n+1+rum,n=0,where p,q,r ?R,and m,n ? N.We pay our attention in the third chapter to investigating the oscillatory prop-erty for the delay partial difference equation um+2,n+um,n+2-pum,n+qum-?,n-?=0,where p,q ?R,and m,n,?,?,?N.In the fourth chapter,we study the oscillatory property for the delay partial difference equation um+2,n+pum,n+2+qum,n+rum-?,n-?=0,where p,q,r ?R,and m,n,?,? ? N.The stress in the fifth chapter is to study the oscillatory property for the ad-vanced partial difference equation Pum+2,n+qum,n+2-um,n+rum+?,n+?=0,where p,g,r ?R,m,n,?,??N,and p2 + q2 + r2?0.All of the above researches are accompanied with computer simulations.The experimental results not only illustrate the oscillatory behavior of the solutions,but also validate the presented results.