Abstract
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, withm≥3boundary conditions,u¨(t)∈F(t,u(t),u˙(t))a.e. on[0,1]; u˙(0)=0, u(1)=∑i=1m-2aiu(ξi), where0<η<θ<1,0<ξ1<ξ2<⋯<ξm-2<1andFis a multifunction from[0,1]×ℝn×ℝnto the nonempty compact convex subsets ofℝn. We have results that improve earlier theorems.
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