Abstract
This paper is concerned with controlled nonlinear impulsive evolution equations with nonlocal conditions. The existence of PC-mild solutions is proved, but the uniqueness cannot be obtained. By constructing approximating minimizing sequences of functions, the existence of optimal controls of systems governed by nonlinear impulsive evolution equations is also presented.
Highlights
1 Introduction Since the end of last century, impulsive evolution equations and impulsive optimal controls have attracted much attention because many evolutional processes are subject to abrupt changes in the form of impulses
How does one look for suitable optimal controls when the uniqueness of solutions of controlled impulsive equations cannot be obtained? In spite of some attempts and efforts, the previous method is not entirely satisfactory
The existence of optimal controls of systems governed by nonlocal impulsive evolution equations with the initial condition x( ) + g(x) = x seems to be rarely involved
Summary
Since the end of last century, impulsive evolution equations and impulsive optimal controls have attracted much attention because many evolutional processes are subject to abrupt changes in the form of impulses (see [ – ]). It is different from the usual approach that the Banach contraction mapping theory is applied directly to prove the existence of optimal controls if the uniqueness of feasible pairs cannot be obtained. In Section , the existence results of controlled nonlocal evolution equations are obtained.
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