围长为2的偶数阶本原极小强连通有向图的1一指数集

本文研究了围长为2的n阶本原极小强连通有向图的1-指数集,证明了：当n（≥4）为偶数时,E（1）={4,5,6,7,…,2n-4）,无缺数段。     

On the pth moment exponential stability criteria of neutral stochastic functional differential equations

The paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the Ito type. This investigation can be very complicated, even in many special cases, by using usual methods based on Lyapunov functionals. In this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations.     

Multipeak solutions to the Bahri-Coron problem in domains with a shrinking hole

We construct positive and sign changing multipeak solutions to the pure critical exponent problem in a bounded domain with a shrinking hole, having a peak which concentrates at some point inside the shrinking hole (i.e. outside the domain) and one or more peaks which concentrate at interior points of the domain. These are, to our knowledge, the first multipeak solutions in a domain with a single small hole.     

Multiple positive solutions for a semilinear elliptic equation with critical Sobolev exponent

In this paper, we study a class of semilinear elliptic equations with Hardy potential and critical Sobolev exponent. By means of the Ekeland variational principle and Mountain Pass theorem, multiple positive solutions are obtained.     

On (p a , p b , p a , p a-b )-Relative Difference Sets

This paper provides new exponent and rank conditions for the existence of abelian relative (p ^a,p ^b,p ^a,p ^a–b)-difference sets. It is also shown that no splitting relative (2^2c,2^d,2^2c,2^2c–d)-difference set exists if d > c and the forbidden subgroup is abelian. Furthermore, abelian relative (16, 4, 16, 4)-difference sets are studied in detail; in particular, it is shown that a relative (16, 4, 16, 4)-difference set in an abelian group G Z₈ × Z₄ × Z₂ exists if and only if exp(G) 4 or G = Z₈ × (Z₂)³ with N Z₂ × Z₂.     

On a semilinear Schrödinger equation with critical Sobolev exponent

We consider the semilinear Schrödinger equation , , where , are periodic in for , 0$">, is of subcritical growth and 0 is in a gap of the spectrum of . We show that under suitable hypotheses this equation has a solution . In particular, such a solution exists if and .

     

谐和随机噪声联合作用下Van der PolDuffing振子的参数主共振

研究了Van der Pol－Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题。用多尺度法分离了系统的快变项，并求出了系统的最大Liapunov指数和稳态概率密度函数，还分析了失稳、分 叉和跳跃现象，讨论了系统的阻尼项、非线性项、随机项和确定性参激强度等参数对系统响应的影响。数值模拟表明所提出的方法是有效的。     

Critical exponents for nonlinear diffusion equations with nonlinear boundary sources

This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q₀ and the critical Fujita exponent qc for the problems considered, and show that q₀=qc for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q₀<qc for the one-dimensional case.     

具超临界指数p-Laplace方程解的存在性

证明了一类具超临界指数p-Laplace方程在全空间和有界域上正解的存在性,给出了解的一些估计.