Weak mean attractors and invariant measures for stochastic Schrödinger delay lattice systems

• Published in: Journal of dynamics and differential equations Vol. 35; no. 4; pp. 3201 - 3240
• Main Authors: Chen, Zhang, Wang, Bixiang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Hilbert space; Invariants; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Tightness; Time lag; 37L55; 60H10; Invariant measure; Asymptotic compactness; Stochastic Schrödinger lattice system; Weak pullback mean attractor; Time delay; Tail-estimate; 37L40

In this paper, we study the long term dynamics of the stochastic Schrödinger delay lattice systems when the nonlinear drift and diffusion terms are both locally Lipschitz continuous. Based on the well-posedness of the system, we first prove the existence and uniqueness of weak pullback mean random a...