Random attractors for multi-valued multi-stochastic delayed p-Laplace lattice equations

The dynamical behaviour of the stochastic non-autonomous p-Laplace lattice equation driven by variable delays, random viscosity, multiplicative noise and non-Lipschitz nonlinearity is concerned. The existence of global solutions for the equation is proved, while the solutions are possibly multi-valued and generate a multi-valued dynamical system. The existence of a pullback attractor is shown. Moreover, the measurability of the pullback attractor as well as the multi-valued cocycle is proved by using the weak continuity of the discrete p-Laplace operator and a countable decomposition of the Wiener probability space.