GLOBAL EXPONENTIAL ATTRACTION FOR MULTI-VALUED SEMIDYNAMICAL SYSTEMS WITH APPLICATION TO DELAY DIFFERENTIAL EQUATIONS WITHOUT UNIQUENESS

摘要

We first prove the existence of a compact positively invariant set which exponentially attracts any bounded set for abstract multi-valued semidynamical systems. Then, we apply the abstract theory to handle retarded ordinary differential equations and lattice dynamical systems, as well as reaction-diffusion equations with infinite delays. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true.