时滞细胞神经网络方程概周期解的存在唯一性

主要考虑了一类连续神经网络系统离散化情况.在一定条件下得到了这类方程概周期解的存在性和唯一性以及其全局吸引性.作为应用,最后给出一个例子.     

一类散度形式椭圆型方程很弱解的唯一性

运用Hodge分解方法,选择适当的检验函数,证明了一类散度形式椭圆型偏微分方程在grand Sobolev空间很弱解的唯一性.     

Jordan李超代数的一些性质

代数A称为不可分解的,如果A不能分解成理想的直和.证明了满足C(L_o)=C(L)={0}的Jordan李超代数L一些重要性质.     

A Positive Solution of Mixed Non-Linear Fractional Delay Differential Equations with Integral Boundary Conditions

In this paper, we study mixed non-linear fractional delay differential equations with integral boundary conditions. We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation of the second kind. Further, we establish existence and uniqueness of positive solutions for the problem using Guo-Krasnoseleskii''s fixed point theorem and Banach contraction principle.     

微分方程解的存在区间的确定

从六个方面说明了确定一阶微分方程解的存在区间的方法.     

A strong uniqueness theorem for planar vector fields

This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.Dedicated to Constantine Dafermos on his 60^th birthdayWork supported in part by CNPq, FINEP, FAPESP and a Research Incentive Fund grant of Temple University.     

Finite element analysis of thermally coupled nonlinear Darcy flows

We consider a coupled system describing nonlinear Darcy flows with temperature dependent viscosity and with viscous heating. We first establish existence, uniqueness, and regularity of the weak solution of the system of equations. Next, we decouple the coupled system by a fixed point algorithm and propose its finite element approximation. Finally, we present convergence analysis with an error estimate between continuous solution and its iterative finite element approximation.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Carleman Estimates for Second-Order Hyperbolic Equations

In the space of variables (x, t) ∈ ? ⁿ⁺¹, we consider a linear second-order hyperbolic equation with coefficients depending only on x. Given a domain D ? ? ⁿ⁺¹ whose projection to the x-space is a compact domain Ω, we consider the question of construction of a stability estimate for a solution to the Cauchy problem with data on the lateral boundary S of D. The well-known method for obtaining such estimates bases on the Carleman estimates with an exponential-type weight function exp(2τ?(x, t)) whose construction faces certain difficulties in case of hyperbolic equations with variable coefficients. We demonstrate that if D is symmetric with respect to the plane t = 0 then we can take ?(x, t) to be the function ?(x, t) = s ²(x, x ⁰) ? pt ², where s(x, x ⁰) is the distance between points x and x ⁰ in the Riemannian metric induced by the differential equation, p is some positive number less than 1, and the fixed point x ⁰ can either belong to the domain Ω or lie beyond it. As for the metric, we suppose that the sectional curvature of the corresponding Riemannian space is bounded above by some number k ₀ ≥ 0. In case of space of nonpositive curvature the parameter p can be taken arbitrarily close to 1; in this case as p → 1 the stability estimates lead to a uniqueness theorem which describes exactly the domain of the solution continuation through S. It turns out that, in case of space of bounded positive curvature, construction of a Carleman estimate is possible only if the product of k ₀ and sup _x∈Ω s ²(x, x ⁰) satisfies some smallness condition.     

奇异非线性二阶三点边值问题正解的存在唯一性

本文研究了一类奇异非线性二阶三点边值问题，通过摄动技巧和比较原理获得了所论问题正解的存在唯一性。     

含两组状态变量等变分歧问题开折的唯一性和稳定性

基于奇点理论中光滑映射芽的接触等价,讨论多参数等变分歧问题关于接触等价的开折的唯一性和稳定性.将这种等变分歧问题的状态变量分为两组,其中一组的诸状态变量可以独立地变化,而属于另一组的诸状态变量在变化过程中依赖于前一组中的诸状态变量.得出了在接触等价下,满足一定条件的等变分歧问题的万有开折是唯一的,并且给出了一定条件下等变分歧问题开折稳定的一个充要条件.