Exponential Attrators For Klein-Gordon-Schrodinger Lattice System And Running Periodic Solution Of Equation Of Pendulum' Type With Segment Linear Periodic Function

This paper consists of two parts. This first one is related the existence of exponential attractor for the KGS lattice system. The second one is concerned with the existence of a running periodic solution of a second order equation of pendulums type with a segment linear periodic function. The pendulums type is the well-known model for a pendulum with friction driven by a periodic torque, and its behavior of dynamical about equilibrium and running periodic solution has been recently considered.This paper is organized as follows: In chapter 1, we introduce the background of infinite dimensional dynamical systems, lattice dynamical systems and a class of second order differential equations with a damping coefficient. In chapter 2, we introduce some basic concepts and notations that relate to the paper. In chapter 3, utilizing proposition of existence of exponential attractor of KGS lattice system, we mainly prove the existence of exponential attractor of KGS lattice system. In chapter 4, By the methods of differential equation existing the upper and lower solution, we prove the existence of a running periodic solution of a second order equation of pendulums type with a segment linear periodic function.