Upper Semicontinuity of Pullback Attractors for Singular Perturbated Delay Lattice Systems
摘要
In this paper, we mainly consider the upper semicontinuity of the pullback attractors for the singular perturbated second order nonautonomous delay lattice systems with respect to the coefficient of the second derivative term. First we prove the existence of the pullback attractors for the second order delay lattice systems and the corresponding first order delay lattice systems under certain conditions, respectively. Second, we consider the upper semicontinuity of the pullback attractors under Hausdorff semidistance as the coefficient of the second order derivative term tends to zero and a positive constant. The former show the relationship between the pullback attractors for second order and the corresponding first order nonautonomous delay lattice systems. The used methods are mainly introducing suitable new norms, decomposing the linear parts and delay term in the systems, constructing an auxiliary sets in the phase space of the second order nonautonomous delay lattice systems such that each sections of the pullback attractor of the first order nonautonomous delay lattice systems being naturally embedded into these sets as the first components. Finally, we consider the existence, exponentially stability and upper semicontinuity of the singleton pullback attractors for the second order and first order nonautonomous delay lattice systems under some conditions.