This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in...This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.展开更多
In this paper, we study the exponential stability of the zero solution to a neutral diferential equation. By applying the Lyapunov-Krasovskiì functional approach, we prove a result on the stability of the zero so...In this paper, we study the exponential stability of the zero solution to a neutral diferential equation. By applying the Lyapunov-Krasovskiì functional approach, we prove a result on the stability of the zero solution. The result we obtained extends and generalizes the existing ones in the previous literature. Comparing with the previous results, our result is new and complements some known results.展开更多
By the averaging method of frst order, we study in this work the limit cycles for a class of second order diferential equations and Dufng diferential equations which can be seen as a particular perturbation of the har...By the averaging method of frst order, we study in this work the limit cycles for a class of second order diferential equations and Dufng diferential equations which can be seen as a particular perturbation of the harmonic oscillator.展开更多
A backward stochastic diferential equation is discussed in this paper. Under some weaker conditions than uniformly Lipschitzian condition given by Pardoux and Peng(1990), using Picard interaction and Cauchy sequence, ...A backward stochastic diferential equation is discussed in this paper. Under some weaker conditions than uniformly Lipschitzian condition given by Pardoux and Peng(1990), using Picard interaction and Cauchy sequence, the existence and uniqueness of the solutions to the backward stochastic diferential equation.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12171361)the Humanity and Social Science Youth foundation of Ministry of Education(Grant No.20YJC790174)。
文摘This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.
文摘In this paper, we study the exponential stability of the zero solution to a neutral diferential equation. By applying the Lyapunov-Krasovskiì functional approach, we prove a result on the stability of the zero solution. The result we obtained extends and generalizes the existing ones in the previous literature. Comparing with the previous results, our result is new and complements some known results.
文摘By the averaging method of frst order, we study in this work the limit cycles for a class of second order diferential equations and Dufng diferential equations which can be seen as a particular perturbation of the harmonic oscillator.
基金Supported by NNSF of China(10171010)Scientifc Research Fund of Zhejiang Provincial Education Department(Y201329578)
文摘A backward stochastic diferential equation is discussed in this paper. Under some weaker conditions than uniformly Lipschitzian condition given by Pardoux and Peng(1990), using Picard interaction and Cauchy sequence, the existence and uniqueness of the solutions to the backward stochastic diferential equation.
