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75��0,?t��[0,tf]. (15g) Here, Bv is a weight factor that describes the patient's acceptance level of chemotherapy. We choose the control parameter as a class of piecewise continuous functions defined for all t such that 0 �� v(t) �� vmax GSK2126458 chemical structure an Optimal Solution To prove the existence of Glucosidases the optimal solution of (15a)�C(15g), we use the results of Fleming and Rishel [29, Theorem 4.1, pages 68-69] and Lukes [30, Theorem 9.2.1, page 182]. Theorem 5 . �� There exists an optimal solution (x*, v*) �� W1,��([0, tf], R4) �� L��([0, tf], R) for the optimal control problem (15a)�C(15g) such that J(v?)=max?v��Vad?J(v), (17) where x* = [E*, T*, N*, u*]T if the following conditions are satisfied. The set of admissible state is nonempty. The admissible set Vad is nonempty, convex, and closed. The right-hand side of the state system is bounded by a linear combination of the state and control variables. The integrand, L(E, T, v) = (E(t) ? T(t) ? (Bv/2)[v(t)]2), of the objective functional is a concave on Vad. There exist constants h2, h3 > 0, and b > 1 such that L(E, T, v) �� h2 ? h3(|v|)b. Proof �� In order to verify the above conditions, we should first prove the existence of the solution for system of the state equations (15b)�C(15e). LY317615 cell line Since ��T(t ? ��)/(�� + T(t ? ��)) form (E(t)T(t)N(t)u(t))��