The optimal regulator equations are obtained using the maximum principle.
From (49) we infer, using the maximum principle, that z n + 1 ≫ 0 in [ 0, 1 ].
Furthermore, the uniform validity of the solutions is proved by using the maximum principle.
end{aligned} (5.4) Using the maximum principle, we have (vequiv K).
The uniform validity of the solutions is proved by using the maximum principle in Section 3.
Using the maximum principle, we can get that u is nonnegative in x and (t in[0,t^)).
Especially, Li [19] considered fully nonlinear elliptic equations on smooth domains, and Berestycki and Nirenberg [20] found a way to deal with general equations with nonsmooth domains using the maximum principles on domains with small measure.
We use the maximum principle for an integro-differential operator to derive the uniqueness of the inverse problem.
We use the maximum principle, Theorem 34 (1) if (c=0) and Theorem 16 if (c>0), to obtain (varphi _2le 0) on ([c,d]]), which is a contradiction.
We use the maximum principle, Theorem 16 with the interval (, a,bb),) and the function (,F m,p,r,x),) replaced by (, c,dd),) and (,F m,p,r,x +mu _2r), respectively, to obtain (varphi _2le 0) on ([c,d]]), which is a contradiction.
Since A is positive definite, it follows that G λ ( 0 ) = ( A G λ, G λ ) > 0. We use the maximum principle and suppose that for some n ≠ 1, G λ ( n ) < 0. Since G λ ( n ) → 0 as n → ∞ and G λ ( 0 ) > 0, it follows that G λ attains a global strictly negative minimum at some point n > 1 (the case n < - 1 is similar).
