The existence of pullback exponential attractors for nonautonomous dynamical system and applications to nonautonomous reaction diffusion equations

First we establish some sufficient conditions for the existence of pullback exponential attractors by using $omega-$limit compactness in the framework of process. Then we provide a new method to prove the existence of pullback exponential attractors. As a simple application, we prove the existence of pullback exponential attractors for nonautonomous reaction diffusion equations in $H_0^1$.