Semistable extremal ground states for nonlinear evolution equations in unbounded domains ✩

In this paper we show that dissipative reaction–diffusion equations in unbounded domains posses extremal semistable ground states equilibria, which bound asymptotically the global dynamics. Uniqueness of such positive ground state and their approximation by extremal equilibria in bounded domains is also studied. The results are then applied to the important case of logistic equations. © 2007 Elsevier Inc. All rights reserved.