On equiwellset minimum problems

A sequence of minimum problems given on a metric space, together with a limit problem, is called equiwellset if every problem has exactly one solution, if the values converge, and if any asymptotically minimizing sequence converges to the solution of the limit problem. When all problems are equal we get the classical definition of Tyhonov. A metric characterization of equiwellposedness is given that generalizes results of Vainberg for a single problem. Differential characterizations are also obtained extending a result of Asplund-Rockafellar. Applications are given to the epsilon method and to the perturbations of the linear quadratic problem.Work partially supported by Laboratorio di Matematica Applicata del C.N.R. presso l'Università di Genova.