On the Kneser property for reaction–diffusion equations in some unbounded domains with an H−1H−1-valued non-autonomous forcing term

In this paper, we prove the Kneser property for a reaction–diffusion equation on an unbounded domain satisfying the Poincaré inequality with an external force taking values in the space H−1H−1. Using this property of solutions we check also the connectedness of the associated global pullback attractor.We study also similar properties for systems of reaction–diffusion equations in which the domain is the whole RNRN.Finally, the results are applied to a generalized logistic equation.