包含次临界和临界Sobolev指数的Schrdinger-Possion方程的正解

讨论了一类包含次临界和临界Sobolev指数的Schrdinger-Possion方程解的存在性.应用Nehari流形和变分方法,在不同情况下,得到了方程至少存在一个解.     

含临界位势与临界参数的超线性椭圆型方程

本文考虑一类含临界位势与临界参数的超线性椭圆型方程解的存在性.本文应用Morse理论,考虑非线性项f(x,s)在零点附近以及无穷远处的性质,给出了方程在某个新的Sobolev-Hardy空间中解的存在性.     

三维迁移方程的临界参数与临界通量

中子迁移理论中,描述给定的物理系统的两个参数--两个基本的本征值起着重要的作用[1][2],基本时间参数是非定态中子迁移问题的具最大实部的一个实的时间本征值,临界参数是定态中子迁移问题具最大绝对值的一个实的定态本征值.研究与基本时间参数和临界参数的存在性,及相应的非负本征函数的存在性和唯一性有关的一些数学问题至今仍有不少尚待解决[3][4].在文献[5][6]中,我们讨论了基本时间参数及其相应的正本征函数的问题.本文我们研究三维迁移系统的临界参数的存在性,及其相应的本征函数的非负性和唯一性,并给出用迭代法求解它们的收敛性证明以及收敛速度的阶的估计.     

包含次临界和临界指数以及加权函数的Kirchhoff方程

本文讨论了一类包含次临界和临界Sobolev指数及加权函数的Kirchhoff方程解的存在性.应用Nehari流形和变分方法,在不同情况下,得到了方程至少存在一个非平凡解.     

具有临界和非临界人为故障的人-机系统解的存在唯一性及半离散化

研究了具有临界和非临界人为故障率,且修复时间任意分布的可修复的人-机系统模型.利用初等方法将系统转换为8维Banach空间下的Volterra积分方程,得到系统非负解存在且唯一.并讨论了系统解的逼近.     

带有临界型非线性项的强阻尼波动方程

研究一类带有临界型非线性项的强阻尼波动方程.通过选择合适的状态空间,证明了算子矩阵[OA-IηAθ]的扇形性,评估了带有临界型增长指数的非线性项的临界性,并且研究了弱解的局部与整体存在性和正则性.     

具临界位势和权函数的非线性双调和问题

本文考虑具有临界位势和临界权函数的四维非线性重调和问题,证明非平凡解的存在性.     

带有次临界或临界增长的分数阶Schr?dinger-Poisson方程组非平凡解的存在性

研究了一类带有次临界或临界增长的分数阶Schr?dinger-Poisson方程组,应用Nehari流形方法得到了非平凡解的存在性.     

R2中含临界位势的非线性椭圆问题

考虑R²中的含临界位势的非线性椭圆方程齐次Dirichlet问题. 通过建立一常数为最佳的含权不等式, 确定了临界位势, 并讨论了含临界位势的Laplace方程特征值问题. 通过建立含一个奇点的解的Pohozaev型恒等式并结合Cauchy-Kovalevskaya定理得到了含临界位势非线性椭圆型方程有奇点的解的不存在性结果. 此外, 利用山路定理和特征值的性质得到了这一问题多重解的存在性的一系列结果.     

临界h-边-连通图的临界度

图G称为k-临界h-边-连通的,若h=λ(G)且对每个k顶点集{u1,…,uk}有λ(G-{u1,…,ui})≤λ(G-{u1,…,ui-1})-1,I≤k.若G是k-临界h-边-连通但不(k 1)-临界h-边-连通,则记之为(h*,k*)λ.本文证明了:存在(h*,k*)λ图的充要条件是(1)1≤k≤[(h 1)/2],h≡0,1,2(mod 4);1≤k≤[(h-1)/2],h≡3(mod 4);或(2)k=h,G=Kk 1.     

具有分布反馈和边界反馈的非均质Timoshenko梁的指数镇定性

讨论具有分布反馈控制和边界反馈控制的非均质Timoshenko梁的指数镇定问题.首先利用已有的关于线性分布参数系统的渐进稳定性判据,证明所论梁系统的能量可仅由一个分布反馈控制指数镇定.进而利用频域分片乘子方法,在所论梁系统同时具有分布反馈控制和边界反馈控制的条件下,证明其相应的闭环系统能量指数稳定.     

On the stability of Timoshenko-type systems with internal frictional dampings and discrete time delays

In this paper, we consider a vibrating system of Timoshenko-type in a bounded one-dimensional domain under Dirichlet–Dirichlet or Dirichlet–Neumann boundary conditions with one or two discrete time delays and one or two internal frictional dampings. First, we show that the system is well posed in the sens of semigroup theory. Second, we prove the exponential stability regardless to the speeds of wave propagation of the system if the weights of the time delays are smaller than the ones of the corresponding dampings, respectively. However, when the weight of one time delay is not smaller than the one of the corresponding damping, we prove the exponential stability in case of equal-speed wave propagation, and the polynomial stability in the opposite case.     

Weakly invariant sets of hybrid systems

We consider a mathematical model of a hybrid system in which the continuous dynamics generated at any point in time by one of a given finite family of continuous systems alternates with discrete operations commanding either an instantaneous switching from one system to another, or an instantaneous passage from current coordinates to some other coordinates, or both operations simultaneously. As a special case, we consider a model of a linear switching system. For a hybrid system, we introduce the notion of a weakly invariant set and analyze its structure. We obtain a representation of a weakly invariant set as a union of sets of simpler structure. For the latter sets, we introduce special value functions, for which we obtain expressions by methods of convex analysis. For the same functions, we derive equations of the Hamilton-Jacobi-Bellman type, which permit one to pass from the problem of constructing weakly invariant sets to the control synthesis problem for a hybrid system.     

Existence result for a gradient-type elliptic system involving a pair of p(x) and q(x)-Laplacian operators

In this paper, we deal with a typical gradient elliptic system involving a pair of p(x) and q(x)-Laplacian operators. Furthermore, the system may have nonlinearities with sign-changing. Precisely, we are interested in seeking at least one weak nontrivial solution. In this way, we establish explicitly a pair of lower and upper solutions having radial forms and related to the system. By applying the theory of monotone operators, we show that the system possesses at least one non-trivial and bounded solution.     

相依修理的可修排队系统 MAP/PH(M/PH)/2

系统地研究了两个不同并行服务台的可修排队系统MAP/PH(M/PH)/2,其中两个不同的服务台拥有一个修理工.若其中一台处于修理状态,则另一台失效后就处于待修状态.利用拟生灭过程理论,我们首先讨论了两个服务台的广义服务时间的相依性,然后给出了系统的稳态可用度和稳态故障度,最后得到了系统首次失效前的时间分布及其均值.     

On Bers Generating Functions for First Order Systems of Mathematical Physics

Considering one of the fundamental notions of Bers’ theory of pseudoanalytic functions the generating pair via an intertwining relation we introduce its generalization for biquaternionic equations corresponding to different first-order systems of mathematical physics with variable coefficients. We show that the knowledge of a generating set of solutions of a system allows one to obtain its different form analogous to the complex equation describing pseudoanalytic functions of the second kind and opens the way for new results and applications of pseudoanalytic function theory. As one of the examples the Maxwell system for an inhomogeneous medium is considered, and as one of the consequences of the introduced approach we find a relation between the time-dependent one-dimensional Maxwell system and hyperbolic pseudoanalytic functions and obtain an infinite system of solutions of the Maxwell system. Other considered examples are the system describing force-free magnetic fields and the Dirac system from relativistic quantum mechanics.     

一类具细焦点的三次系统极限环的唯一性

继续相关文献的工作,给出与二次系统Ⅰ相伴的一类三次系统在奇点N(0,1/n)的焦点量公式,证明了系统在细焦点N外围至多有一个极限环,同时证明了当N或O为细焦点时,系统在另一个焦点外围无极限环,结合相关文献的结论,说明了具有细焦点的该系统在全平面至多有一个极限环.     

Expected waiting times in polling systems under priority disciplines

In this paper, we analyse a service system which consists of several queues (stations) polled by a single server in a cyclic order with arbitrary switchover times. Customers from several priority classes arrive into each of the queues according to independent Poisson processes and require arbitrarily distributed service times. We consider the system under various priority service disciplines: head-of-the-line priority limited to one and semi-exhaustive, head-of-the-line priority limited to one with background customers, and global priority limited to one. For the first two disciplines we derive a pseudo conservation law. For the third discipline, we show how to obtain the expected waiting time of a customer from any given priority class. For the last discipline we find the expected waiting time of a customer from the highest priority class. The principal tool for our analysis is the stochastic decomposition law for a single server system with vacations.     

Stabilization of string system with linear boundary feedback

In this paper we consider the uniform stabilization of a vibrating string with Neumann-type boundary conditions. Herein we do not consider a controller stabilizing the system, but emphasize the simplicity and effectiveness of the controller. We adopt the linear feedback control law, which comprises both boundary velocity and position, and prove that the closed loop system is dissipative and asymptotically stable. By asymptotic analysis of frequency of the closed loop system, we give asymptotic expression of the frequencies and the Riesz basis property of eigenvectors and generalized eigenvectors of the system operator under some conditions, and hence obtain the exponential stability of the closed loop system. We show that, for a particular case, the system may be super-stable in subspace of a codimensional one. From the above result, we conclude that one can design a much simpler linear controller by choice of parameters such that the closed loop system is of Riesz basic properties and exponentially stable.     

Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities

In this paper, we present a smoothing Newton-like method for solving non-linear systems of equalities and inequalities. By using the so-called max function, we transfer the inequalities into a system of semismooth equalities. Then a smoothing Newton-like method is proposed for solving the reformulated system, which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.