Upper semicontinuity of uniform attractors for singular perturbed second order nonautonomous delay lattice systems

Abstract

In this article, we consider the upper semicontinuity of the uniform attractors for the singular perturbed second order nonautonomous delay lattice systems driven by the almost periodic forces as the coefficient of second order derivative term tends to zero under the Hausdorff semidistance. First we prove the existence of uniform attractors for the second order and the corresponding first order nonautonomous delay lattice systems. Then we establish some prior uniform estimations of solutions. Finally we study the upper semicontinuity of the uniform attractors as the coefficient of second order derivative term tends to zero which showing the relationship between the uniform attractors for second order and the corresponding first order nonautonomous delay lattice systems.

Keywords

• singular perturbed second order delay lattice system
• uniform attractor
• upper semicontinuity
• continuous process
• almost periodic function