The Asymptotic Behavior Of Non-autonomous Schr(?)dinger Lattice System With Multiplicative White Noise

In this paper,we mainly studied two aspects contents.On the one hand,we stud-ied the existence of the random exponential attractor of non-autonomous Schr(?)dinger stochastic lattice system with multiplicative white noise.On the other hand,we studied the existence and the exponential stability of the random attractor of the non-autonomous delay Schr(?)dinger lattice system with multiplicative white noise.Three parts of this paper are as follows:The first part,chapter 1 of this paper,is composed of the present situation,the background,main contents,basic concepts about the problems and the inequalities we need.The second part,the core of this paper,consists of chapter 2 and chapter 3.In the second chapter,we considered the non-autonomous Schr(?)dinger lattice system with multiplicative white noise and verified the existence of a random exponential attractor According to the criteria of existence of a random exponential attractor,we first trans-ferred the considered stochastic system into a random system without noise through the O-U process.Then the difference between two solutions was decomposed into two parts,and the expectations of some random variables were estimated.Finally,the existence of a random exponential attractor was verified.In the third chapter,we mainly stud-ied the random attractor of the non-autonomous delay Schr(?)dinger lattice system with multiplicative white noise about its existence and exponential stabilityThe third part,the last chapter of this paper,summarized the whole article and provided further research suggestions.