Second-order nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators and optimal controls on Banach spaces

Authors:
Y. Peng;X. Xiang;W. Wei
Affiliations:
Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, a class of second-order nonlinear impulsive integro-differential equations of mixed type whose principle is time-varying generating operators with unbounded perturbation on Banach spaces is considered. Discussing the perturbation of time-varying operator matrix and constructing corresponding the evolution system generated by operator matrix, we introduce the reasonable mild solution of second-order nonlinear impulsive integro-differential equations of mixed type and prove the existence of mild solutions. The existence of optimal controls for a Lagrange problem of systems governed by the second-order nonlinear impulsive integro-equations of mixed type is also presented. An example is given for demonstration.