Positive Ground State Solutions for Schrödinger-Poisson System with General Nonlinearity and Critical Exponent

In this paper, we consider the following Schrödinger-Poisson system begin{equation*}begin{cases} -Delta u + etaphi u = f(x,u) + u^5,& xinOmega, -Deltaphi=u^2,& xinOmega,u = phi =0,& xin partialOmega, end{cases}end{equation*} where $Omega$ is a smooth bounded domain in $R^3$, $eta=pm1$ and the continuous function $f$ satisfies some suitable conditions. Based on the Mountain pass theorem, we prove the existence of positive ground state solutions.     

一类多量子比特完全可分态的可分表示及应用

可分量子态能够写成乘积态的凸组合.通过可分量子态的可分表达式可以更好地理解量子态的数学结构.给出了一类多量子比特完全可分量子态的可分分解表示.此外,通过该类可分态的完全可分表示得到了一类阶数为2k的正交矩阵.     

广义倒易定理及其应用

推广Betti倒易定理的概念,建立了非耦联系统和耦联系统的广义倒易定理,它们适用于具有不同本构关系的两个变形体。当该两变形体的本构关系相同且为线弹性时,该非耦联系统的广义倒易定理即成为Betti倒易定理。同时,应用该两个广义倒易定理于弹性力学中的模拟计算。     

铰接结构极限状态函数的自动生成

本文在结构可靠性分析中,以铰接结构为例,推导了结构连续变更定理,并将其用于生成杆件的极限状态函数,避免了由于结构拓扑不断变更引起的总刚度阵多次组装及多次求逆运算.引入了结构退化为机构的新判据,算例结果令人满意.     

Positive solutions of a general discrete boundary value problem

In this paper, the existence of positive solutions for a nonlinear general discrete boundary value problem is established. Such results extend and improve some known facts for the two-point and three-point boundary value problems. Particularly, the boundary value conditions can be nonlinear and the method is new. For explaining the main results, some numerical examples are also given.     

含瞬时态、具有突变率的广义生-灭Q-矩阵(Ⅱ)

研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,在Q_(E_0)非零流出下,给出易于验证的Q过程存在性准则,并构造出全部Q过程和全部诚实Q过程,证明了不需附加任何条件,所有诚实Q过程都是遍历的,并求出其遍历测度以及给出诚实Q过程可配称的充要条件。最后给出两个例子以说明本文的结果易于验证。     

PERIODIC SOLUTIONS OF BAM NETWORKS WITH STATE DEPENDENT DELAYS

We use Krasnosel'skii's fixed point theorem to show that the following BAM networks with state dependent delays has a periodic solution.     

绝对稳定性中的共轭定理及应用

本文证明了非定常非线性控制系统在有限扇形角内存在共轭定理．即当时，与这两个系统具有相同的绝对稳定性．由此推出对偶定理、降维原理并给出它们的应用．     

SINGULARLY PERTURBED NONLINEARELLIPTIC SYSTEMS IN STRIP DOMAIN

Singularly perturbed problems for the nonlinear dliptie systems in a strip domain are considered. Under suitabla conditions, by using the comparison theorem, the existence andasymptotic behavior of solution for the boundary value problems are studied.     

On a theorem of Marcinkiewicz and Zygmund

Let {ϕn(x)} be an orthonormal system on the closed interval [0,1], and let ∥ϕ _n ∥_∞ ≤M _n . In 1937 Marcinkiewicz and Zygmund obtained an estimate of the norm inL _q [0,1] of the sum of the series ∑ _n=1 ^∞ c _n ϕ _n (x) under the condition that {M _n } is monotone increasing. In this paper it is shown that this condition cannot be discarded. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 386–390, March, 1998. The author wishes to thank V. I. Kolyada for setting the problem and for his permanent attention to this work.     

一类奇摄动非线性椭圆型系统

本文讨论了一类在带形区域中的非线性椭圆型系统的奇轻边值问题,在适当的条件下 比较定理台相应边值问题解的存在性和斩近性态作了研究。     

A new proof of a theorem on optimal control of switched systems

Recently Sorin C. Bengea and Raymond A. DeCarlo [Sorin C. Bengea, Raymond A. DeCarlo, Optimal control of switching systems, Automatica J. IFAC 41 (2005) 11-27] have offered a key result that the set of trajectories of the two-switched system is dense in the set of trajectories of the embedded system. This result was proven by means of relaxed controls and the Chattering Lemma. In this paper we use the Lyapunov theorem to give a new simple proof.     

多种群生态竞争-捕食时滞系统正周期解的全局吸引性

本文利用比较定理结合Ｌｉａｐｕｎｏｖ泛函的方法,　讨论一类具有多个时滞的多种群生态竞争－捕食系统正周期解的存在性和全局吸引性,得到了一些新的结果,　并举例说明条件的可行性．     

Globally Smooth Solutions to an Inhomogeneous Quasilinear Hyperbolic System Arising in Chemical Engineering

In this paper we have obtained the existence of globally smooth solutions to an inhomogeneous nonstrictly hyperbolic system u_t - (v(1 - u))_x = 0, v_t + (\frac{1}{2}v² - c_0u)_x = f(u,v) by employing the characteristic method and the fixedpoint theorem in Banach spaces.     

Existence and multiplicity results for the nonlinear Schrödinger-Poisson systems

In this paper, we study the existence and multiplicity results for the nonlinear Schrödinger-Poisson systems

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