一类一阶泛函微分方程解的存在性与分支

本文研究方程ｘ’（ｔ）＝（ｘ２（ｔ）－μ）ｘ（ｘ（ｔ））μ≤０（１）解的性态。当μ＜０时，我们得到与Ｅｄｅｒ［１］和ｗａｎｇ［２］相类似的结论，也得到一些新的性质；当μ＝０时，我们得到全新的结论，证明方程（１）存在两端均不可延拓到∞的严格单调饱和强解，μ＝０是方程（１）的分支值。     

Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type

We discuss the existence of minimal and maximal solutions for a class of first order nonlinear impulsive functional integro-differential equations of mixed type with anti-periodic boundary conditions. The main tool of study is the monotone iterative technique.     

模糊积分方程(英文)

参考文献［１］利用单调迭代方法研究了模糊微分方程最小解与最大解的存在性，本文在较弱的条件下研究了模糊积分方程的上述问题．本文主要结果的证明比文［１］更简洁．     

粘性系数依赖于密度的Korteweg型不可压流体的强解问题

研究一类Korteweg型不可压流体模型的强解问题.针对粘性系数依赖于密度的情形,当初始值满足兼容性条件(9)对,证明了强解的局部存在性和唯一性.我们在这指出,本文允许初始真空存在.     

Banach空间二阶非线性积分-微分方程组初值问题(英文)

使用半序方法和新的比较结果,研究Banach空间二阶非线性积分-微分方程组初值问题最大最小解的存在性.     

Remarks on Maximal Attractors for the Compressible Navier-Stokes Equations of Viscous and Heat Conductive Fluid

This paper is concerned with the existence of maximal attractors in Hi (i = 1, 2,4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn(n = 2,3).     

Existence for the thermoelastic thermistor problem

We study a new model for the thermistor problem that consists of a system of dynamic thermoelasticity equations of displacement and a stationary charge conservation equation of electrical current. The heat source generated by Joule heating is quadratic in the gradient of the electrical potential. This system is nonlinear and degenerate since the electrical conductivity is assumed to be temperature dependent and vanishes at large temperatures. We establish the existence of a very weak solution, the so-called “capacity solution” for the model. The proof is based on regularization and time retarding.     

Systems of matrix rational differential equations arising in connection with linear stochastic systems with Markovian jumping

In this paper, a class of systems of matrix nonlinear differential equations containing as particular cases the systems of coupled Riccati differential equations arising in connection with control of some linear stochastic systems is considered.The system of differential equations considered in this paper are converted in a suitable nonlinear differential equation on a finite-dimensional Hilbert space adequately choosen.This allows us to use the positivity properties of the linear evolution operator defined by the linear differential equations of Lyapunov type.Our aim is to investigate properties of stabilizing and bounded solutions of the considered differential equations and to obtain some conditions ensuring the existence of such solutions.Conditions providing the existence of a maximal solution (minimal solution respectively) with respect to some classes of global solutions are presented. It is shown that if the coefficients of the equations are periodic functions all these special solutions (stabilizing, maximal, minimal) are periodic functions, too.Whenever possible the probabilistic arguments were avoided and so the results proved in the paper appear as results in the field of differential equations with interest in themselves.     

一类非线性Dirac方程组

本文寻求方程组 i sum from j=0 to 3 r~j _jΨ+L(Ψ■)Ψ=0的某些含两个零分量的解.     

Hypergeometric Solutions of Trigonometric KZ Equations Satisfy Dynamical Difference Equations

The trigonometric KZ equations associated to a Lie algebra g depend on a parameter λ∈h where h⊂g is a Cartan subalgebra. A system of dynamical difference equations with respect to λ compatible with the KZ equations is introduced by V. Tarasov and the second author (2000, Internat. Math. Res. Notices15, 801-829). We prove that the standard hypergeometric solutions of the trigonometric KZ equations associated to sl_N also satisfy the dynamical difference equations.     

A note on global existence of weak solutions to the compressible magnetohydrodynamic equations with Coulomb force

In this note, for the case of , we prove the existence of global-in-time finite energy weak solution of the equations of a two-dimensional magnetohydrodynamics with Coulomb force, where γ denotes the adiabatic exponent. The value is the optimal lower bound of γ to establish global-in-time finite energy weak solution under current frame.