Banach空间二阶非线性奇异微分方程的解

文中讨论了Banach空间中一类右端具有奇异性的二阶非线性微分方程的边值问题,利用不动点方法,获得了该边值问题解的存在性定理.最后还给出了相应的例子.     

关于双特征Beltrami方程

该文研究空间Ｂｅｌｔｒａｍｉ方程的推广形式，即双特征Ｂｅｌｔｒａｍｉ方程．利用外微分形式与矩阵的外代数等工具，将双特征Ｂｅｌｔｒａｍｉ方程转化为一个非齐次的狆 调和方程，转化过程中只用到加于特征矩阵的一致椭圆型条件．然后验证了算子犃满足的条件：Ｌｉｐｓｃｈｉｔｚ型条件、单调不等式、齐次性条件以及算子犅满足的控制增长条件．并利用得到的狆 调和方程，给出了双特征Ｂｅｌｔｒａｍｉ方程广义解分量函数的弱单调性结果．     

A multiclass network with non-linear, non-convex, non-monotonic stability conditions

We consider a stochastic queueing network with fixed routes and class priorities. The vector of class sizes forms a homogeneous Markov process of countable state space Z⁶ ₊. The network is said “stable” (resp.“unstable”) if this Markov process is ergodic (resp. transient). The parameters are the traffic intensities of the different classes. An unusual condition of stability is obtained thanks to a new argument based on the characterization of the “essential states”. The exact stability conditions are then detected thanks to an associated fluid network: we identify a zone of the parameter space in which diverging, fluid paths appear. In order to show that this is a zone of instability (and that the network is stable outside this zone), we resort to the criteria of ergodicity and transience proved by Malyshev and Menshikov for reflected random walks in Z⁶ ₊ (Malyshev and Menshikov, 1981). Their approach allows us to neglect some “pathological” fluid paths that perturb the dynamics of the fluid model. The stability conditions thus determined have especially unusual characteristics: they have a quadratic part, the stability domain is not convex, and increasing all the service rates may provoke instability (Theorem 1.1 and section 7). This revised version was published online in June 2006 with corrections to the Cover Date.     

Dual and Feller-Reuter-Riley transition functions

In this paper, we investigate duality and Feller-Reuter-Riley (FRR) property of continuous-time Markov chains (CTMCs). A criterion of dual q-functions is given in terms of their q-matrices. For a dual q-matrix Q, a necessary and sufficient conditions for the minimal Q-function to be a FRR transition function are also given. Finally, by using dual technique, we give a criterion of FRR Q-functions when Q is monotone.     

Heron平均幂型推广的Schur凸性

讨论了两个正数a,b的H eron平均幂型推广在R2+上的单调性和Schur凸性,并得到了两个新的不等式.     

Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions

We present some complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions. This extends some known results due to S.-L. Qiu and M. Vuorinen.     

Studying Baskakov–Durrmeyer operators and quasi-interpolants via special functions

We prove that the kernels of the Baskakov–Durrmeyer and the Szász–Mirakjan–Durrmeyer operators are completely monotonic functions. We establish a Bernstein type inequality for these operators and apply the results to the quasi-interpolants recently introduced by Abel. For the Baskakov–Durrmeyer quasi-interpolants, we give a representation as linear combinations of the original Baskakov–Durrmeyer operators and prove an estimate of Jackson–Favard type and a direct theorem in terms of an appropriate K-functional.     

Approximation of the Navier–Stokes system with variable viscosity by a system of Cauchy–Kowaleska type

In this paper, we study the existence of weak solutions when n?4 of the mixed problem for the Navier–Stokes equations defined in a bounded domain Q using approximation by a system of Cauchy–Kowaleska type. Periodical solutions are also analyzed. Copyright © 2008 John Wiley & Sons, Ltd.     

Monotonicity principle in the rayleigh problem for an isothermally incompressible fluid

The convection of an isothermally incompressible fluid in a horizontal layer with free undeformable boundaries kept at a constant temperature is considered. Under the fairly common assumptions of the temperature dependence of the specific volume, it is shown that the monotonicity principle holds and that the spectrum of critical Rayleigh numbers is countable and prime. Models with linear and quadratic temperature dependences of the specific volume are given as examples. The results on the spectrum of the critical Rayleigh numbers are also valid for some other boundary conditions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 35–42, September–October, 2007.     

Multiple periodic solutions of a class of p-Laplacian

By using the recent generalization of coincidence degree method, the existence of multiple periodic solutions for a class of p-Laplacian is obtained under the existence of strict upper and lower solutions.