Banach空间中非线性脉冲积分微分方程的正解

借助于锥理论，本文讨论Ｂａｎａｃｈ空间中非线性脉冲积分微分方程的解，给出一阶脉冲微分方程存在唯一正解的条件及混合型脉冲积分微分方程至少具有两解的条件。     

Banach空间中N阶脉冲积分-微分方程边值问题的解

运用Monch不动点定理，获得了Banach空间中一类N阶非线性混合型脉冲积分-微分方程边值问题解的存在性．最后给出一个三阶无穷脉冲积分-微分方程边值问题的例子来说明文中所给的条件是合理的．     

具有脉冲积分条件的一次脉冲积分-微分方程混合系统

本文讨论具有脉冲积分条件的脉冲积分-微分方程混合类型的极值解的存在性.主要工具是上下解和单调迭代技术.     

一类具有时滞的中立型分数阶脉冲微分方程解的存在唯一性

基于分数阶脉冲微分方程解的新的积分形式,利用Banach不动点定理和Schauder不动点定理研究了在脉冲条件下一类具有时滞的中立型分数阶微分方程的柯西问题,得出了这类微分方程解的存在性和唯一性.     

Banach空间非线性脉冲Volterra型积分方程和积分-微分方程的可解性

本文在较宽松的条件下,研究了Banach空间非线性脉冲Volterra型积分方 程和脉冲积分一微分方程解的存在性,建立了新的存在性定理,本质上改进了某些已 知的结果.     

Banach空间中的一阶脉冲积分-微分方程边值问题

讨论了抽象空间中的一阶脉冲积分-微分方程的边值问题，利用上下解讨论了解的存在性．     

Banach空间中脉冲积分-微分方程的初值问题

给出了 Banach空间中一阶线性脉冲积分 -微分方程初值问题解的存在唯一性的一个新证法 ,改进了已有结果 .利用它讨论了一阶非线性脉冲积分 -微分方程初值问题的解 ,所得结果大大推广了已有的相关结果 .     

脉冲中立型时滞微分方程的振动性

本文证明了线性脉冲中立型微分方程解的振动性等价于一类线性非脉冲中立型时滞微分方程解的振动性．应用这一结果,建立了线性脉冲中立型方程解振动性的显式判据．这些判别条件,显著地改进了已有的结果．     

一阶脉冲时滞积分微分方程边值问题

本文研究了一类一阶脉冲时滞积分微分方程边值问题解的性质. 利用迭代分析方法, 得到了该类边值问题解的存在性、唯一性和平凡解一致稳定的充分条件, 推广了已有积分微分方程周期边值问题解的结论.     

一阶脉冲时滞积分微分方程边值问题

本文研究了一类一阶脉冲时滞积分微分方程边值问题解的性质.利用迭代分析方法,得到了该类边值问题解的存在性、唯一性和平凡解一致稳定的充分条件,推广了已有积分微分方程周期边值问题解的结论.     

Analytic expansion of periodic solutions of integro-differential systems

We constructively obtain conditions for the existence of periodic solutions of systems of integro-differential equations in the degenerate case. By using integro-differential equations with a parameter, we construct an analytic representation of the solutions and obtain estimates for the convergence rate of iterative processes and for the exact solutions.     

Convergence and Mean-Square Stability of Exponential Euler Method for Semi-Linear Stochastic Delay Integro-Differential Equations

In this paper, the numerical methods for semi-linear stochastic delay integro-differential equations are studied. The uniqueness, existence and stability of analytic solutions of semi-linear stochastic delay integro-differential equations are studied and some suitable conditions for the mean-square stability of the analytic solutions are also obtained. Then the numerical approximation of exponential Euler method for semi-linear stochastic delay integro-differential equations is constructed and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent with strong order $\frac{1}{2}$ and can keep the mean-square exponential stability of the analytical solutions under some restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results.     

Banach空间中脉冲积分-微分方程的迭代解

利用单调迭代技术,本文首先讨论了Banach空间一阶脉冲积分-微分方程初值问题最大解与最小解的存在性.在此基础上,讨论了右端项中带有一阶导数的二阶脉冲积分-微分方程初值问题最大解与最小解的存在性.最后的例子说明对导数的限制条件是可验证的.     

Delay integro-differential inequalities with initial time difference and applications

Some comparison results for delay integro-differential inequalities starting from different initial points are formulated. The monotone iterative technique is applied to formulate sufficient conditions for existence of extremal solutions of delay integro-differential equations with initial time difference.     

Rank criteria for the controllability of a boundary-value problem for a linear system of integro-differential equations with pulse influence

We determine necessary and sufficient conditions for the solvability of boundary-value problems for a linear system of integro-differential equations with pulse influence. We prove theorems on the existence and integral representation of solutions of linear second order integral-sum Volterra equations and linear systems of integro-differential equations with pulse influence at fixed times. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 723–730, June, 2000.     

Global solutions of nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces

In this paper, by using the generalization of Darbo’s fixed point theorem, we establish the existence of global solutions of an initial value problem for a class of second-order impulsive integro-differential equations of mixed type in a real Banach space. Our results generalize and improve on the results of Guo et al. [F. Guo, L.S. Liu, Y.H. Wu, P. Siew, Global solutions of initial value problems for nonlinear second-order impulsive integro-differential equations of mixed type in Banach spaces, Nonlinear Anal. 61 (2005) 1363–1382] in the sense that the conditions for existence of global solution in our theorem is simpler and less strict. To demonstrate the application of the theorem, we give the global solutions of two mixed boundary value problems for two classes of fourth order impulsive integro-differential equations.     

马氏相依风险模型红利折现的矩

该文讨论常数红利边界下的马氏相依模型的矩的问题. 首先, 推导出破产前全部红利的折现期望、红利折现的高阶矩所满足的积分-微分方程组及相应的边界条件. 然后, 通过构造特殊的初始条件, 利用Laplace变换, 在给定的一类索赔分布下, 得到上面方程组的显式解. 最后, 给出两状态下指数索赔的数值计算结果.     

Square-mean almost periodic solutions to some stochastic evolution equations

This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called "Acquistapace–Terreni" conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.     

Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations

Abstract

In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration.     

A note on the fractional Cauchy problems with nonlocal initial conditions

Of concern is the Cauchy problems for fractional integro-differential equations with nonlocal initial conditions. Using a new strategy in terms of the compactness of the semigroup generated by the operator in the linear part and approximating technique, a new existence theorem for mild solutions is established. An application to a fractional partial integro-differential equation with a nonlocal initial condition is also considered.