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A class of nonlinear impulsive differential equation and optimal controls on time scales

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  • This paper is mainly concerned with a class of optimal control problems of systems governed by the nonlinear impulsive differential equation on time scale. The reasonable weak solution of nonlinear impulsive differential equation on time scale is introduced and the existence and uniqueness of the weak solution and its properties are presented. By $L^{1}-$strong$-$weak lower semicontinuity of integral functional on time scale, we give the existence of optimal controls. Using integration by parts formula on time scale, the necessary conditions of optimality are derived. An example on mathematical programming is also presented for demonstration.
    Mathematics Subject Classification: 37M10, 35D05, 49K25, 90C46.

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