Asymptotic Stability Of Nonlinear Partial Difference Equations Of A Class Of Multi Delay

The partial difference equations (PDES)are difference equation thatinvolve functions of two or more independent variables. Such equations occur frequentlyin finding the approximate solutions of partial differential equations by finite differencemethods, and in studying on molecular orbits and mathematical physics equationsetc.This paper are divided into three chapters.In chapter 1 the historical background, present searching situation of the researchproblem and the major research work of this paper are described.In chapter 2 basic definitions and lemma this paper involves are introduced. Inorder to prove our main theorem, a convergent sequence are established in lemma 2and the corresponding proof is made.In chapter 3 the main content of this paper are contained. First, the oscillationand permanence of the solutions of partial differential equations are studied and thecorresponding sufficient conditions are established. Next, the solutions of partial difference equations and the convergent sequences in lemma 2 are compared. By means ofmathematical induction method, uniform stability of the solutions of partial differentialequations are obtained. Finally, the attraction of the the solutions of partial differenceequations is prove by using properties of supremum and infimum, thus the uniformasymptotic stability of the solutions of partial difference equation are obtained.