Weak mean attractors of stochastic p-Laplacian delay lattice systems driven by nonlinear noise

This paper deals with the existence and uniqueness of weak pullback mean random attractors for a class non-autonomous stochastic p-Laplacian delay lattice systems with local Lipschitz nonlinear terms driven by nonlinear noise defined on the entire integer set Z. We first establish the global well-posedness to non-autonomous stochastic p-Laplacian delay lattice system in C([τ,∞),L2(Ω,ℓ2)) when the nonlinear diffusion terms and drift terms are locally Lipschitz continuous functions, based on the uniform estimates of approximate solutions in a finite time-interval as well as an appropriate stopping time. We then define a mean random dynamical system via the solution operators and prove the existence and uniqueness of weak pullback mean random attractors in product Hilbert space L2(Ω,F;ℓ2)×L2(Ω,F;L2((−ρ,0),ℓ2)) under the condition that the constant λ in the system is relatively large.