一类三阶拟线性微分方程非振动解的渐近性

主要讨论的是一类三阶拟线性微分方程(p(t)|u″|~(α-1)u″)′+q(t)|u|~(β-1)u=0其中α0,β0,p(t)和q(t)是定义在区间[a,∞)上的连续函数,且满足当t≥a时p(t)0,q(t)0.当t→∞时此方程满足∫_a~∞1/((p(t))~(1/α))dt=∞的特殊非振动解存在的充分必要条件.     

超线性时滞微分方程解的振动性

研究一阶超线性时滞微分方程x′(t) p(t)[x(t—γ)]^α＝0(α＞1)解的振动性及非振动性,获得了保证其所有解振动的“almost sharp”准则,并应用所得结果于混合型时滞微分方程x′（t） ∑^ni=1pi（t）[x（t-γi]^αi=0,得到一族振动准则。     

常微分方程解的普遍唯一性定理和整体存在性定理

§1.引言考虑常微分方程组 dx/dt=f(t,x),(E)其中x=(x~1,…,x~n)表示n维向量,f=(f~1,…,f~n)表示n维实的向量函数。 Kamke在1930年的专著中得到如下的一个普遍唯一性定理: 设ω(t,r)是定义在0相似文献   

二阶含阻尼项可化为“积分小”系数的微分方程解的振动性质

本文考虑下列二阶微分方程 (r(t)x′(t))′ q(t)x′(t) p(t)x(t)=0. (1) 和 (r(t)x′(t))′ q(t)x′(t) p(t)f(x(g(t)))=0 (2)解的振动性质。我们给出了方程(1)非振动解存在的充要条件和方程(2)存在振动解的充分判据。     

具有正负系数的中立型方程的振动性

讨论中立型方程d/dt[x(t)-R(t)x(t-r)] P(t)x(t-t)-Q(t)x(t-δ）=0,（*）其中P,Q,R∈C[（to,∞）,R∧ ）,r,τ,δ∈（0,∞）,τ≥δ,在允许R（t） ∫∧tt=τ δQ（u）du-1变号的情况下得到（*）的所有解振动的判据。     

具有正负系数的中立型时滞微分方程

考虑具有正负系数的中立型时滞微分方程d/dt[x(t)-C(t)x(t-r)]+P(t)x(t-r)-Q(t)x(t-δ)=0(1)我们获得了(1)的所有解振动的“sharp”条件,即条件在系数C(t),P(t)及Q(t)为常数时是充分必要的.作为其推论也大大地推广并改进了文[2—5,7—9]的相应定理.     

某些一阶非齐次中立型微分差分方程的振动性

该文讨论了 d/dt[x(t) cx(t-τ)] P(t)x(t-σ) f(t)=0,t≥t_0一阶非齐次中立型微分差分方程的振动性.得到了一些方程振动的充分条件,推广了某些齐次方程的振动结果.     

食物有限的时滞种群模型的振动性

将考虑两类具有变时滞非线性有限食物种群模型N′(t)=r(t)N(t)K-N(p(t))/K+s(t)N(σ(t)),t≥ 0和N′(t)=r(t)N(t)K-Nα(p(t))/K+s(t)Nα(σ(t)),t≥ 0,的振动性,其中α>0,ρ(t)≤t,σ(t)≤t.我们的工作推广并改进了相关文献的结果.     

L^1空间中紧算子的一个注记

由于具有有界可测核函数的积分算子不能保证在L[0,1]^1上是紧算子,本文证明了当d(s)和b(t)是有界可测函数,G(s,t)是连续函数时,一类弱奇异核函数K1(s,t)=d(s)G(s,t)b(t)/|s-t|^α(0<α<1)对应的积分算子K1:(K(1φ))(s)=∫0^1 K1(s,t)φ(t)dt在L([0,1])^1上产生一个紧算子,并给出了一个具体的弱奇异函数对应积分算子的紧性证明.     

一类n维中立型非线性时超微分方程组解的振动性

本应用中立型时超不等式解振动的判别准则和变换技巧，研究了一类n维中立型非线性时超微分方程组{d/dt[Xi-c(t)Xi(t r)] ∑k=1^m1∑j=1^n aij^k(t)Xj(t τk)-∑s=1^m2∑j=1^nbji^s(t)Xj(t δs) bif(σ(t ηi)))=0 σ(t)=∑t=1^n Csxi(t)(i=1,2,…,n)解的振动性,获得了其解振动的判别准则。     

正定矩阵标准型的复合矩阵的一般形式

实对称正定矩阵的复合矩阵正定性的研究已有结论,但对于一般意义下的正定矩阵的复合矩阵是否仍然是正定的研究需要利用一般的正定矩阵的标准形的复合矩阵进行讨论,给出了一般公式及具体算法,为讨论其复合矩阵的正定性提供了基础条件.     

Completely positive tensors in the complex field

In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the complex completely positive tensor are given. A semidefinite algorithm is also proposed for checking whether a complex tensor is complex completely positive or not. If a tensor is not complex completely positive, a certificate for it can be obtained; if it is complex completely positive, a complex completely positive decomposition can be obtained.     

On the Existence of Positive Eigenvalues for Linear and Nonlinear Equations with Indefinite Weight

We prove the existence of positive eigenvalues for two types of equations having an indefinite weight. We consider the linear case, and we show the existence of a positive principal eigenvalue corresponding to a positive eigenfunction. For the nonlinear case, we show that the set of positive eigenvalues is an unbounded interval, and that the corresponding eigenfunctions are positive.     

Global Existence of Positive Solutions for Volterra Integral Equations

ＧｌｏｂａｌＥｘｉｓｔｅｎｃｅｏｆＰｏｓｉｔｉｖｅＳｏｌｕｔｉｏｎｓｆｏｒＶｏｌｔｅｒｒａＩｎｔｅｇｒａｌＥｑｕａｔｉｏｎｓＷａｎｇＳｈｕ（王术）；ＷａｎＣｈｕｎｌｉｎ（万春林）；ＺｈａｎｇＫｕｎ（张锟）（ＨｅｍａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎ...     

Generic existence and uniqueness of positive eigenvalues and eigenvectors

We consider a closed cone of positive operators on an ordered Banach space and prove that a generic element of this cone has a unique positive eigenvalue and a unique (up to a positive multiple) positive eigenvector. Moreover, the normalized iterations of such a generic element converge to its unique eigenvector.     

BCK-代数的Ω-模糊正定关联理想

给定一个集合Ω,引入了BCK-代数的Ω-模糊正定关联理想的概念,给出了一些恰当的例子,讨论了BCK-代数的Ω-模糊理想与Ω-模糊正定关联理想的关系.利用模糊正定关联理想,刻画了Ω-模糊正定关联理想.反之,模糊正定关联理想通过Ω-模糊正定关联理想来构造.证明了Ω-模糊正定关联理想(Ω-模糊理想)的同态原象仍是Ω-模糊理想(Ω-模糊理想).     

关于非线性矩阵方程$X^s-A^*X^{-t}A=Q$的Hermitian正定解及其扰动估计

In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X^s - A^＊X^-tA = Q are studied, where Q is a Hermitian positive definite matrix, s and t are positive integers. The existence of a Hermitian positive definite solution is proved. A sufficient condition for the equation to have a unique Hermitian positive definite solution is given. Some estimates of the Hermitian positive definite solutions are obtained. Moreover, two perturbation bounds for the Hermitian positive definite solutions are derived and the results are illustrated by some numerical examples.     

On the Spectra of Striped Sign Patterns

Sign patterns consisting of some positive and some negative columns, with at least one of each kind, are shown to allow any self-conjugate spectrum, and thus to allow any inertia. In the case of the n ×n sign pattern with all columns positive, given any self-conjugate multiset consisting of n -1 complex numbers supplemented by a sufficiently large positive number, it is shown how to construct a positive normal matrix whose spectrum is this multiset. Thus, the positive sign pattern allows any inertia with at least one positive eigenvalue.     

On the Spectra of Striped Sign Patterns

Sign patterns consisting of some positive and some negative columns, with at least one of each kind, are shown to allow any self-conjugate spectrum, and thus to allow any inertia. In the case of the n × n sign pattern with all columns positive, given any self-conjugate multiset consisting of n m 1 complex numbers supplemented by a sufficiently large positive number, it is shown how to construct a positive normal matrix whose spectrum is this multiset. Thus, the positive sign pattern allows any inertia with at least one positive eigenvalue.     

On Positive Linear Volterra-Stieltjes Differential Systems

We first introduce the notion of positive linear Volterra-Stieltjes differential systems. Then, we give some characterizations of positive systems. An explicit criterion and a Perron-Frobenius type theorem for positive linear Volterra-Stieltjes differential systems are given. Next, we offer a new criterion for uniformly asymptotic stability of positive systems. Finally, we study stability radii of positive linear Volterra-Stieltjes differential systems. It is proved that complex, real and positive stability radius of positive linear Volterra-Stieltjes differential systems under structured perturbations coincide and can be computed by an explicit formula. The obtained results in this paper include ones established recently for positive linear Volterra integro-differential systems [36] and for positive linear functional differential systems [32]-[35] as particular cases. Moreover, to the best of our knowledge, most of them are new. The first author is supported by the Alexander von Humboldt Foundation.