Abstract
We consider the existence and properties of the global attractor for a class of reaction-diffusion equation∂u/∂t-Δu-u+κ(x)|u|p-2u+f(u)=0, in Rn×R+; u(x,0)=u0(x), in Rn. Under some suitable assumptions, we first prove that the problem has a global attractorAinL2(Rn). Then, by using theZ2-index theory, we verify thatAis an infinite dimensional set and it contains infinite distinct pairs of equilibrium points.
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