... u(t, a) has a unique c ritical point c (a) in (a, b (a )),and at this point, u(t, a) obtains a local maximum value.Lemma 3.1 Assume that (F2) holds, then j(t, a) >0for all t Î (a, c (a) ).Proof. We ... 2011:38http://www.boundaryvalueproblems.com/content/2011/1/38Page 4 of 9Since τ (a) to be the last zero of j(t, a )in (a, b (a) ), the behavior of j(t, a) in(τ (a) ,b (a) ) can be classified into two cases as follows:(i) ... for all t Î (a, t0]. With the initial point t0replace by r >t0, for an appropriate valuer, the same proof can be reapplied as often as necessary to give uniqueness of any con-tinuation...