Copyright © 2009 Caisheng Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the long-time behavior of
solution for the m-Laplacian equation ut−div(|∇u|m−2∇u)+λ|u|m−2u+f(x,u)=g(x) in RN×R+, in which the nonlinear term f(x,u) is a function like f(x,u)=−h(x)|u|q−2u with h(x)≥0, 2≤q<m, or f(x,u)=a(x)|u|α−2u−h(x)|u|β−2u with a(x)≥h(x)≥0 and α>β≥m. We prove the existence of a
global (L2(RN),Lp(RN))-attractor for any p>m.