Abstract

This paper is concerned with the second order nonlinear impulsiveevolution differential equations perturbed by unbounded operator onBanach space. Discussing the perturbation of time-varying operatormatrix and constructing the corresponding evolution system generatedby operator matrix we introduce the reasonable mild solution ofsecond order nonlinear impulsive evolution differential equationsand prove the existence of mild solutions. Existence of optimalcontrols for a Lagrange problem of systems governed by the secondorder nonlinear impulsive evolution equations is also presented. Anexample is given for demonstration.

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