For a continuous, increasing function ω ： R^＋ →R^＋／{0} of finite exponential type, this paper introduces the set Z（A, ω） of all x in a Banach space X for which the second order abstract differential equation ...For a continuous, increasing function ω ： R^＋ →R^＋／{0} of finite exponential type, this paper introduces the set Z（A, ω） of all x in a Banach space X for which the second order abstract differential equation （2） has a mild solution such that [ω（t）]^-1u（t,x） is uniformly continues on R^＋, and show that Z（A, ω） is a maximal Banach subspace continuously embedded in X, where A ∈ B（X） is closed. Moreover, A[z（A,ω） generates an O（ω（t）） strongly continuous cosine operator function family.展开更多
Integrated semigroups which are not exponentially bounded have been studied. The integrated solutions of inhomogeneous and nonlinear abstract Caucby problems are discussed. The reults extends and improves the theorems...Integrated semigroups which are not exponentially bounded have been studied. The integrated solutions of inhomogeneous and nonlinear abstract Caucby problems are discussed. The reults extends and improves the theorems in [1].展开更多
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
We consider the higher-order Cauchy problem (ACP_n) x^(n)(t)=sum from i=0 to n-1 B_ix^(i)(t)_1x^(i)(0)=x_i for 0≤i≤n-1,where B_i(0≤i≤n-1) are closed linear operators on a Banach space X such that D=∩ i=0 n-1 D(B_...We consider the higher-order Cauchy problem (ACP_n) x^(n)(t)=sum from i=0 to n-1 B_ix^(i)(t)_1x^(i)(0)=x_i for 0≤i≤n-1,where B_i(0≤i≤n-1) are closed linear operators on a Banach space X such that D=∩ i=0 n-1 D(B_i)is dense in X. It is well known that the solvability and the well-posedness of (ACP_n)were studied only in some special cases, such as D(B_(n-1))?D(B_i) for 0≤i≤n-2 by F. Neu-brander and a factoring case by J. T. Sandefur. In this paper, by using some new results ofvector valued Laplace transforms given by W. Arenddt, we obtain some characterizations ofthe solvability and some sufficiency conditions of the well-posedness for general (ACP_n),which generalize F. Neubrander's results and the famous results for (ACP_1)展开更多
In this paper,we first give a sufficient and necessary condition for M= to generate an exponentially bounded =-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy pr...In this paper,we first give a sufficient and necessary condition for M= to generate an exponentially bounded =-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem （（ACP<sub>2</sub>） for short） in some sense.Then we use these results and those in [1] to discuss the C-（exponential） wellposedness of a kind of （ACP<sub>2</sub>） with application backgrounds,and develop the results in [2].展开更多
For injective, bounded operator C on a Banach space X , the author defines the C -dissipative operator, and then gives Lumer-Phillips characterizations of the generators of quasi-contractive C -semigro...For injective, bounded operator C on a Banach space X , the author defines the C -dissipative operator, and then gives Lumer-Phillips characterizations of the generators of quasi-contractive C -semigroups, where a C -semigroup T(·) is quasi-contractive if ‖T(t)x‖‖Cx‖ for all t0 and x∈X . This kind of generators guarantee that the associate abstract Cauchy problem u′(t,x)=Au(t,x) has a unique nonincreasing solution when the initial data is in C(D(A)) (here D(A) is the domain of A ). Also, the generators of quasi isometric C -semigroups are characterized.展开更多
In this paper, we apply the contraction mapping theorem to establish some bounded and unbounded additive perturbation theorems concerning local C-semigroups. Some growth conditions of perturbations of local C-semigrou...In this paper, we apply the contraction mapping theorem to establish some bounded and unbounded additive perturbation theorems concerning local C-semigroups. Some growth conditions of perturbations of local C-semigroups axe also established.展开更多
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
This paper is concerned with the global existence of solutions for abstract retarded functional differential equations （RFDEs） with infinite delay, via a fixed point approach. Some sufficient conditions are establis...This paper is concerned with the global existence of solutions for abstract retarded functional differential equations （RFDEs） with infinite delay, via a fixed point approach. Some sufficient conditions are established under which the existence of a globally mild solution are obtained by using Leray-Schauder.展开更多
The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are e...The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown.展开更多
文摘For a continuous, increasing function ω ： R^＋ →R^＋／{0} of finite exponential type, this paper introduces the set Z（A, ω） of all x in a Banach space X for which the second order abstract differential equation （2） has a mild solution such that [ω（t）]^-1u（t,x） is uniformly continues on R^＋, and show that Z（A, ω） is a maximal Banach subspace continuously embedded in X, where A ∈ B（X） is closed. Moreover, A[z（A,ω） generates an O（ω（t）） strongly continuous cosine operator function family.
文摘Integrated semigroups which are not exponentially bounded have been studied. The integrated solutions of inhomogeneous and nonlinear abstract Caucby problems are discussed. The reults extends and improves the theorems in [1].
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.
文摘We consider the higher-order Cauchy problem (ACP_n) x^(n)(t)=sum from i=0 to n-1 B_ix^(i)(t)_1x^(i)(0)=x_i for 0≤i≤n-1,where B_i(0≤i≤n-1) are closed linear operators on a Banach space X such that D=∩ i=0 n-1 D(B_i)is dense in X. It is well known that the solvability and the well-posedness of (ACP_n)were studied only in some special cases, such as D(B_(n-1))?D(B_i) for 0≤i≤n-2 by F. Neu-brander and a factoring case by J. T. Sandefur. In this paper, by using some new results ofvector valued Laplace transforms given by W. Arenddt, we obtain some characterizations ofthe solvability and some sufficiency conditions of the well-posedness for general (ACP_n),which generalize F. Neubrander's results and the famous results for (ACP_1)
基金This project is supported by the NNSF of Chinathe Youth Science and Technique Foundation of Shanxi Province China
文摘In this paper,we first give a sufficient and necessary condition for M= to generate an exponentially bounded =-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem （（ACP<sub>2</sub>） for short） in some sense.Then we use these results and those in [1] to discuss the C-（exponential） wellposedness of a kind of （ACP<sub>2</sub>） with application backgrounds,and develop the results in [2].
文摘For injective, bounded operator C on a Banach space X , the author defines the C -dissipative operator, and then gives Lumer-Phillips characterizations of the generators of quasi-contractive C -semigroups, where a C -semigroup T(·) is quasi-contractive if ‖T(t)x‖‖Cx‖ for all t0 and x∈X . This kind of generators guarantee that the associate abstract Cauchy problem u′(t,x)=Au(t,x) has a unique nonincreasing solution when the initial data is in C(D(A)) (here D(A) is the domain of A ). Also, the generators of quasi isometric C -semigroups are characterized.
基金supported by the National Science Council of Taiwan
文摘In this paper, we apply the contraction mapping theorem to establish some bounded and unbounded additive perturbation theorems concerning local C-semigroups. Some growth conditions of perturbations of local C-semigroups axe also established.
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.
基金NNSF of China (No.10271044)NSF of Anhui Province (070416225,2003kj005zd)+1 种基金Talent Foundation of Anhui Province (05025104)Innovation Group of Anhui University
文摘This paper is concerned with the global existence of solutions for abstract retarded functional differential equations （RFDEs） with infinite delay, via a fixed point approach. Some sufficient conditions are established under which the existence of a globally mild solution are obtained by using Leray-Schauder.
基金the Natural Science Foundation of Henan Province (No.994051200).
文摘The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown.
