Abstract
This work is devoted to establish the optimal solutions of impulsive optimal controls for a class of Lagrange problem. Using the approximate method and fixed point theorem, the corresponding semilinear system is solvable under some appropriate assumptions. From the derived results, we propose to construct two kinds of minimizing sequences of approximating solutions to obtain the optimal solutions. The new results obtained here actually give rise to a general technique useful also for other optimal control problems with multiple solutions.
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