Abstract
We present relaxation problems in control theory for the second-order differential inclusions, with four boundary conditions, (sic)(t) epsilon F(t,u(t),(u) over dot (t)) a.e. on [0, 1];u(0) = 0, u(eta) = u(theta) = u(1) and, with m >= 3 boundary conditions, (sic)(t) epsilon F(t,u(t),(u) over dot(t)) a.e. on [0, 1]; (u) over dot(0) = 0, u(1) = Sigma(m-2)(i=1) a(i)u(xi(i)) , where 0 < eta < theta < 1, 0 < xi(1) < xi(m-2) < 1 and F is a multifunction from [0, 1] x R-n x R-n to the nonempty compact convex subsets of R-n. We have results that improve earlier theorems.