The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some...We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some additive perturbation results concerning S（·）. Some growth conditions of the perturbations of S（·） are also established.展开更多
The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous...The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.展开更多
In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosin...In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.展开更多
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
文摘We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some additive perturbation results concerning S（·）. Some growth conditions of the perturbations of S（·） are also established.
文摘The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.
文摘In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
基金This project is supported by the Natural Science Foundation of China and Science Development Foundation of the Colleges and University of Shanghai.
文摘In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.
