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

• 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.
Mathematics Subject Classification: 34G20, 34K30, 35B62, 93C25.

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