Let the optimal control problem: $$\max \int_a^bF(t,x(t),u(t))dt$$ $$x'(t)=g(t,x(t),u(t)) \; for \; all \; t\in [a,b]$$ $$x(a)=A$$ $$x(b)\geq0.$$
Unising the maximum principle and the adjoint state $p(.)$
I want to prove the following transverality condition :
$$p(b)\geq0$$ $$p(b)x(b)=0$$