脉冲输入毒素对具有阶段结构的单种群生存影响的研究

研究了一类小容量污染环境中脉冲输入毒素对具有阶段结构的单种群生存问题,分别找到了种群生存与灭绝的阈值,利用不等式放缩技巧,得到了种群灭绝和持久生存的充分条件.利用MATLAB数值仿真,验证了理论结果的正确性,分析了毒素输入量,毒素输入周期及种群成长时间对种群生存的影响.     

Well‐posedness of initial boundary value problems on longitudinal impact on a composite linear viscoelastic bar

We investigate the correctness of the initial boundary value problem of longitudinal impact on a piecewise‐homogeneous semi‐infinite bar consisting of a semi‐infinite elastic part and finite length visco‐elastic part whose hereditary properties are described by linear integral relations with an arbitrary difference kernel. Introducing nonstationary regularization in boundary conditions and in the contact conditions, the well‐posedness of the considered problem is proved. Copyright © 2017 John Wiley & Sons, Ltd.     

Mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces

Through solving the problem step by step and by applying the method of a C₀ semigroup of operators combined with the Banach contraction theorem, we investigate the existence and uniqueness of a mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces. In addition, an explicit iterative approximation sequence of the mild solution is derived. The assumed conditions in the present theorems are weaker and more general, and the results obtained are the generalizations and improvements of some known results. Examples are also given to illustrate our main results. Copyright © 2017 John Wiley & Sons, Ltd.     

一类具有收获率的脉冲Lotka-Volterra竞争合作系统的八个正概周期解

研究了一类具有收获率的脉冲Lotka-Volterra竞争合作系统的正概周期解.通过利用重合度理论延拓定理、概周期理论和不等式分析技巧,获得了系统至少存在8个正概周期解的充分条件,推广和改进了早期文献的相关结果.     

弹塑性波计算中的光滑粒子法

采用改进的光滑粒子法 ,对脉冲应力载荷下板中弹塑性一维应变波的传播进行了数值计算 ,比较了人工粘性法和通量修正法处理冲击波间断面的效果。结果表明 ,改进的光滑粒子法在应力波数值计算中有良好的精度。     

带阻尼项的三阶脉冲微分方程的振动性与渐近性

解决了一类带阻尼项的三阶脉冲微分方程的非振动解与其一阶、二阶导数的符号关系,用迭代法得到其振动性与渐近性的判别准则,并举例说明准则的有效性.     

一类离散的时滞脉冲切换系统的H_∞二次稳定性

研究了一类离散的时滞脉冲切换系统的H_∞控制问题,利用Lyapunov稳定性理论和线性矩阵不等式方法,给出了离散脉冲切换系统具有性能指标γ的充分条件.     

脉冲系统输入—输出到状态稳定的Lyapunov条件

在一定的条件下,通过对时间域分割成不同的区间段然后应用Lyapunov函数分析方法给出了脉冲系统输入—输出到状态稳定(IOSS)的一个充分条件,另外,讨论了积分输入—输出到状态稳定的情况.     

On the existence and stability for noninstantaneous impulsive fractional integrodifferential equation

In this paper, by means of Banach fixed point theorem, we investigate the existence and Ulam–Hyers–Rassias stability of the noninstantaneous impulsive integrodifferential equation by means of ψ‐Hilfer fractional derivative. In this sense, some examples are presented, in order to consolidate the results obtained.     

Periodic nonautonomous differential equations with noninstantaneous impulsive effects

In this paper, we study a new class of periodic nonautonomous differential equations with periodic noninstantaneous impulsive effects. A concept of noninstantaneous impulsive Cauchy matrix is introduced, and some basic properties are considered. We give the representation of solutions to the homogeneous problem and nonhomogeneous problem by using noninstantaneous impulsive Cauchy matrix, and the variation of constants method, adjoint systems, and periodicity of solutions is verified under standard periodicity conditions. Further, we show the existence and uniqueness of solutions of semilinear problem and establish existence result for periodic solutions via Brouwer fixed point theorem and uniqueness and global asymptotic stability via Banach fixed point theorem.