On the Z2Z2 index of the global attractor for a class of pp-Laplacian equations

By means of the Z2Z2 index, we study the geometrical property of the global attractor for a class of symmetric pp-Laplacian equations ut−div(|∇u|p−2∇u)+|u|r−2u−λ|u|s−2u+f(x,u)=0ut−div(|∇u|p−2∇u)+|u|r−2u−λ|u|s−2u+f(x,u)=0, where λ>0,2≤s≤p,rλ>0,2≤s≤p,r. We first provide, under suitable assumptions, the existence result for the symmetric global attractor AA. Then when 2≤s