ASYMPTOTIC-BEHAVIOR OF THE MINIMA TO A CLASS OF OPTIMIZATION PROBLEMSFOR DIFFERENTIAL-INCLUSIONS

Denoting by S(k)(xi(k)) the set of solutions of the Cauchy problem x i s-an-element-of F(k) (t,x), x(0) = xi(k), for k is-an-element-of N or {infinity}, we prove that, under appropriate assumptions, the sequence {S(k)(xi(k)}k is-an-element-of N converges to S(infinity)(xi(infinity )) in the Kuratowski sense as well as in the Mosco sense. This result together with some facts from GAMMA-convergence theory are used to pro ve a result concerning the existence and the asymptotic behavior of th e minima to the optimization problem min integral T0 [g(k)(t, x(t)) h(k)(t, x(t))]dt + psi(k)(xi), x is-an-element-of S(k)(xi), xi is-an-e lement-of K, with K a compact subset of R(n).