We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion （fBm） with Hurst parameter H ∈ （1/2, 1） in th...We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion （fBm） with Hurst parameter H ∈ （1/2, 1） in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.展开更多
In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-dens...In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.展开更多
The purpose of this paper is to oite an example.We construot a referencesystem(Ω0,0,(0)(t≥0),p0),on which the martingale space ~∞ is not closed andnot dense in the martingale space .To find a suitable closed sub-sp...The purpose of this paper is to oite an example.We construot a referencesystem(Ω0,0,(0)(t≥0),p0),on which the martingale space ~∞ is not closed andnot dense in the martingale space .To find a suitable closed sub-space or a suitable dense sub-space for the ,especially the later is valuable.It has been proved in [1] (Theorem 10) that,if ~∞展开更多
An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existen...An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model.By analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR(susceptible-infected-recovered)epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.展开更多
The controllability of a class of conformable fractional differential system with a non-densely defined linear part satisfying Hille-Yosida condition,is discussed.The existence of mild solution and controllability is ...The controllability of a class of conformable fractional differential system with a non-densely defined linear part satisfying Hille-Yosida condition,is discussed.The existence of mild solution and controllability is established by Banach-fixed point theorem for the system with non-local conditions and control term appearing also in the nonlinear part.An example is discussed to illustrate the results.展开更多
基金Acknowledgements The authors were deeply grateful to the anonymous referees for the careful reading, valuable comments, and correcting some errors, which have greatly improved the quality of the paper. This work was supported by the National Natural Science Foundation of China （Grant No. 11371029）.
文摘We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion （fBm） with Hurst parameter H ∈ （1/2, 1） in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.
基金Project supported by the Tianyuan Foundation of Mathematics (No. A0324624)the National Natural Science Founcation of China (No. 10371040)the Shanghai Priority Academic Discipline.
文摘In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.
文摘The purpose of this paper is to oite an example.We construot a referencesystem(Ω0,0,(0)(t≥0),p0),on which the martingale space ~∞ is not closed andnot dense in the martingale space .To find a suitable closed sub-space or a suitable dense sub-space for the ,especially the later is valuable.It has been proved in [1] (Theorem 10) that,if ~∞
基金supported by National Natural Science Foundation of China (Grant Nos. 11471044 and 11371058)the Fundamental Research Funds for the Central Universities
文摘An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model.By analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR(susceptible-infected-recovered)epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.
文摘The controllability of a class of conformable fractional differential system with a non-densely defined linear part satisfying Hille-Yosida condition,is discussed.The existence of mild solution and controllability is established by Banach-fixed point theorem for the system with non-local conditions and control term appearing also in the nonlinear part.An example is discussed to illustrate the results.
