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January  2008, 4(1): 17-32. doi: 10.3934/jimo.2008.4.17

Second order nonlinear impulsive time-variant systems with unbounded perturbation and optimal controls

Y. Peng 1, and  X. Xiang 1,

1. 

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

Received  June 2006 Revised  August 2007 Published  January 2008

This paper is concerned with the second order nonlinear impulsive evolution differential equations perturbed by unbounded operator on Banach space. Discussing the perturbation of time-varying operator matrix and constructing the corresponding evolution system generated by operator matrix we introduce the reasonable mild solution of second order nonlinear impulsive evolution differential equations and prove the existence of mild solutions. Existence of optimal controls for a Lagrange problem of systems governed by the second order nonlinear impulsive evolution equations is also presented. An example is given for demonstration.
Keywords: Optimal control., Existence, Evolution system, Impulse, Unbounded operator matrix.
Mathematics Subject Classification: 34G20, 34K30, 35B62, 93C2.
Citation: Y. Peng, X. Xiang. Second order nonlinear impulsive time-variant systems with unbounded perturbation and optimal controls. Journal of Industrial and Management Optimization, 2008, 4 (1) : 17-32. doi: 10.3934/jimo.2008.4.17
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