Second-order nonlinear impulsive evolution equations with time-varying generating operators and optimal controls

Abstract:

In this article, the second-order nonlinear impulsive evolution differential equations with time-varying generating operators is considered. Constructing evolution systems generated by time-varying operator matrix, we introduce suitable mild solution of the second-order nonlinear impulsive evolution differential equations. The existence and uniqueness of the mild solutions and the continuous dependence on initial value are proved. The existence of the optimal controls for a Lagrange problem of the systems governed by the second-order nonlinear impulsive evolution equations is also presented. An example is given for demonstration.

Keywords: unbounded operator matrix; evolution system; impulse; existence; compactness; optimal control

Document Type: Research article

DOI: 10.1080/02331930701761391

Affiliations: 1: Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China