In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentiall...In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.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.
We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their appl...We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.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 article, we give sufficient conditions for controllability of some partial neutral functional differential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but ...In this article, we give sufficient conditions for controllability of some partial neutral functional differential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. The results are obtained using the integrated semigroups theory. An application is given to illustrate our abstract result.展开更多
This paper is concerned with the sustained periodic oscillation phenomenon in a threespecies delayed predation system with Holling type II functional response and age structure in top predator.The top predator fertili...This paper is concerned with the sustained periodic oscillation phenomenon in a threespecies delayed predation system with Holling type II functional response and age structure in top predator.The top predator fertility function is regarded as a piecewise continuous smooth function with regard to their maturation period T2.The complicated dynamic behavior is proved by integrated semigroup theory and Hopf bifurcation theorem for semilinear equations with non-dense domain.Through qualitative analysis and bifurcation study of the system,we yield that this system has a nontrivial periodic solution that bifurcates from the positive equilibrium age distribution when bifurcation parameter T passes through some critical values.Numerical simulations are also provided to illustrate theoretically analytical results.展开更多
In this paper,using a fixed point theorem for condensing multi-valued maps,we investigate the existence of integral solutions to a class of nondensely defined neutral evolution impulsive differential inclusions with n...In this paper,using a fixed point theorem for condensing multi-valued maps,we investigate the existence of integral solutions to a class of nondensely defined neutral evolution impulsive differential inclusions with nonlocal conditions in Banach spaces.展开更多
基金This project is supported by the National Science Foundation of China.
文摘In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.
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.
文摘We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.
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supported by TWAS (04-150RG/MATHS/AF/AC)the postdoctoral programme of the "Agence Universitaire de la Francophonie"+1 种基金The second author is supported by NSF of Shanghai (09ZR1408900)Shanghai Leading Academic Discipline Project (B407)
文摘In this article, we give sufficient conditions for controllability of some partial neutral functional differential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. The results are obtained using the integrated semigroups theory. An application is given to illustrate our abstract result.
文摘This paper is concerned with the sustained periodic oscillation phenomenon in a threespecies delayed predation system with Holling type II functional response and age structure in top predator.The top predator fertility function is regarded as a piecewise continuous smooth function with regard to their maturation period T2.The complicated dynamic behavior is proved by integrated semigroup theory and Hopf bifurcation theorem for semilinear equations with non-dense domain.Through qualitative analysis and bifurcation study of the system,we yield that this system has a nontrivial periodic solution that bifurcates from the positive equilibrium age distribution when bifurcation parameter T passes through some critical values.Numerical simulations are also provided to illustrate theoretically analytical results.
基金supported by NNSF of China (No.10371040)Shanghai Priority Academic Discipline
文摘In this paper,using a fixed point theorem for condensing multi-valued maps,we investigate the existence of integral solutions to a class of nondensely defined neutral evolution impulsive differential inclusions with nonlocal conditions in Banach spaces.
