In this paper,we investigate a deteriorating system with single vacation of a repairman.The system is described by infinite differential-integral equations with boundary conditions.Firstly,by using functional analysis...In this paper,we investigate a deteriorating system with single vacation of a repairman.The system is described by infinite differential-integral equations with boundary conditions.Firstly,by using functional analysis methods,especially linear operator’s C;-semigroup theory,we prove the well-posedness of the system and the existence of a unique positive dynamic solution that satisfies probability condition.Next,by analyzing the spectral properties of the system operator,we prove that all points on the imaginary axis except zero belong to the resolvent set of the system operator.Lastly,we prove that zero is not an eigenvalue of the system operator,which implies that the steady-state solution of the system does not exist.展开更多
基金supported by the National Natural Science Foundation of China(No.11761066)。
文摘In this paper,we investigate a deteriorating system with single vacation of a repairman.The system is described by infinite differential-integral equations with boundary conditions.Firstly,by using functional analysis methods,especially linear operator’s C;-semigroup theory,we prove the well-posedness of the system and the existence of a unique positive dynamic solution that satisfies probability condition.Next,by analyzing the spectral properties of the system operator,we prove that all points on the imaginary axis except zero belong to the resolvent set of the system operator.Lastly,we prove that zero is not an eigenvalue of the system operator,which implies that the steady-state solution of the system does not exist.
