The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation...The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.展开更多
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the...This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.展开更多
Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bound...Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bounded C-semigroup (hereinafter abbrevi-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
基金received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement(823731-CONMECH)supported by the National Science Center of Poland under Maestro Project(UMO-2012/06/A/ST1/00262)+3 种基金National Science Center of Poland under Preludium Project(2017/25/N/ST1/00611)supported by the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland(3792/GGPJ/H2020/2017/0)Qinzhou University Project(2018KYQD06)National Natural Sciences Foundation of Guangxi(2018JJA110006)
文摘The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.
基金This work was supported by grants from NNSF of China(No:10271044)Scientific Research Fund of Educational Department of Anhui Province(NSF2003KJ005zd)Teaching Research Fund of Educational Department of Anhui Province(JYXM2003108).
文摘This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
基金Project supported by the National Natural Science Foundation of China.
文摘Let (X;‖ ‖) be a Banach space. By B(X) we denote the set of all bounded linear operators in X. Let C∈B(X) be injective.A strongly continuous family of bounded operators {S(t); t≥0} is called an exponentially bounded C-semigroup (hereinafter abbrevi-
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.
