. On-one, ) I 0) then the equation ao(r)u2 tb"(ae)u+c,(") has the sarne sign as a"(x)for any u ? IR ( respectively, for any u? IR\{-6, (x) l2a,(x)}), and since tr/ is a clf for the system (6.2), in order to have (6.b) we -uJ hu-.,à'à"@)'a'0'.' On the other ha1d

À. If, c) 14e, then B(ae) :0 which implies B(t)A(r) + (1 -B(r))C(ae) : C(x) ?lÀ1

?. Therefore and . Ir-', we have LV(x) : o,(r)u'(x) + b,(ae)u(r) + c, where ur(*) : u(r)u(ae)

. Finallg, then LV (x) : o"(*)u' (x) + b,(x)u(c) + c"(r) has the same sign as a, p.0

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