Two-point problem for vector differential inclusions with discontinuous right-hand side

Given a multifunction $F:[a,b] imes R^n imes R^n o 2^{R^n}$, we consider the two-point problem $$cases{u^{primeprime}(t)in F(t,u(t),u^prime(t))& a.e. in $[a,b]$cr cr u(a)=u(b)=0_{R^n}.cr}$$ We prove an existence theorem for solutions $uin W^{2,p}([a,b],R^n)$, where for each $tin [a,b]$ the multifunction $F(t,cdot,,cdot,)$ can fail to be lower semicontinuous even at all points $(x,y)in R^n imes R^n$. Our result extends a previous result, valid for case where $n=1$ and $F$ does not depend on $u^prime$.