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November  2011, 16(4): 1137-1155. doi: 10.3934/dcdsb.2011.16.1137

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

 1 Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025 2 Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025

Received  October 2010 Revised  March 2011 Published  August 2011

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.
Citation: Yunfei Peng, X. Xiang. A class of nonlinear impulsive differential equation and optimal controls on time scales. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1137-1155. doi: 10.3934/dcdsb.2011.16.1137
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