Relaxation Problems Involving Second-Order Differential Inclusions

Abstract EN

We present relaxation problems in control theory for the second-order differential inclusions, with four boundary conditions, u¨(t)∈F(t,u(t),u˙(t)) a.e.

on [0,1]; u(0)=0, u(η)=u(θ)=u(1) and, with m≥3 boundary conditions, u¨(t)∈F(t,u(t),u˙(t)) a.e.

on [0,1]; u˙(0)=0, u(1)=∑i=1m-2aiu(ξi), where 0<η<θ<1, 0<ξ1<ξ2<⋯<ξm-2<1 and F is a multifunction from [0,1]×ℝn×ℝn to the nonempty compact convex subsets of ℝn.

We have results that improve earlier theorems.