Mean attractors of stochastic delay lattice p-Laplacian equations driven by superlinear noise in high-order product Bochner spaces

This paper is concerned with the existence and uniqueness of mean random attractors of a class non-autonomous stochastic delay p-Laplacian lattice systems defined on a high-dimensional integer set Z(d) driven by a family infinite-dimensional superlinear noise. We first establish the global-in-time existence and uniqueness of the solutions in C([tau,infinity), L-2k(Omega, l(2)(Z(d)))) boolean AND L-q(Omega, L-loc(q) ((tau,infinity), l(q)(Z(d)))) for any k >= 1 when the draft term has an arbitrary polynomial growth rate q > 2 and the coefficient of the noise admits a superlinear growth order <(q)over tilde > is an element of[2, q). We then show that the mean random dynamical system generated by the solution operators has a unique weakly compact and weakly attracting mean random attractor in the highorder product Bochner space L-2k(Omega,F;l(2)(Z(d))) x L-2k (Omega, F; L-2k((-rho, 0),l(2)(Z(d)))), where. is the time delay parameter. The dissipative property of the draft term is employed to carefully controlling the superlinear growth diffusion term. When k = 1, our results are new even in the product Hilbert space L-2(Omega, F; l(2)(Z(d))) x L-2(Omega, F; L-2((-rho, 0), l(2)(Z(d)))). This work can be regard as a further study of mean attractors of stochastic p-Laplacian lattice systems in the works of Wang and Wang (2020) and Chen et al. (2023). (c) 2023 Elsevier Ltd. All rights reserved.