半线性双调和方程解的存在性

考虑了有界光滑区域ΩR~d,d=2,3上的一类半线性双调和方程.非线性项φ（｜▽u｜）是由｜▽u｜~p产生的.应用Schaefer不动点定理证明了当d=2（或d=3）,p满足2≤p〈∞（或2≤p≤6）时,该问题的解是存在的,并且解是局部唯一的.     

一类T形树匹配唯一的充要条件

证明：若m∈Ze^ ,则T形树T(1,m,n）匹配唯一当且仅当n≠m,m 3,2m 5.     

受迫二维广义KdV-Burgers方程的周期行波解

本文研究了受迫二维广义ＫｄＶ－Ｂｕｒｇｅｒｓ方程的周期行波解问题,讨论了解的有界性并给出了解的估计式,进而讨论了周期解的存在性及唯一性.     

抽象半线性发展方程正周期解的存在唯一性

讨论有序Banach空间E中半线性发展方程 u′(t)+Au(t)=f(t,u(t)),t∈R, ω-周期解的存在性,其中A为E中正C0-半群的生成元,f:R×E→E连续,关于t 以ω为周期．我们对相应的线性发展方程建立了周期解的存在唯一性,并对周期解算子的谱半径作了精确估计．借助于这个估计,我们用单调迭代方法获得了半线性发展方程正ω-周期解的存在唯一性．     

非Lipschitz条件下半鞅随机微分方程解的唯一性(英文)

本文研究了非Lipschitz条件下半鞅随机微分方程.利用It(o)分析和Gronwall不等式,探讨了随机微分方程无爆炸解,并证明了随机微分方程解的唯一性.     

Problem of determining the nonstationary potential in a hyperbolic-type equation

We solve the problem of determining the hyperbolic equation coefficient depending on two variables. Some additional information is given by the trace of the direct problem solution on the hyperplane x = 0. We estimate the stability of the solution of the inverse problem under study and prove the uniqueness theorem. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 220–225, August, 2008.     

Global strong solutions for a class of compressible non‐Newtonian fluids with vacuum

We study a class of compressible non‐Newtonian fluids in one space dimension. We prove, by using iterative method, the global time existence and uniqueness of strong solutions provided that the initial data satisfy a compatibility condition and the initial density is small in its H¹‐norm. The main difficulty is due to the strong nonlinearity of the system and the initial vacuum. Copyright © 2010 John Wiley & Sons, Ltd.     

Inverse scattering problem for Sturm–Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition

The inverse problem of the scattering theory for Sturm–Liouville operator on the half line with boundary condition depending quadratic on the spectral parameter is considered. Scattering data are defined, some properties of the scattering data are examined, the main equation is obtained, solvability of the integral equation is proved and uniqueness of algorithm to the potential with given scattering data is studied. Copyright © 2010 John Wiley & Sons, Ltd.     

导数具有三个小函数的亚纯函数

文章主要讨论了两个亚纯函数的K阶导数分担三个小函数时的唯一性问题, 改进了邱凎俤的有关结果.     

四阶非线性奇异抛物方程变分问题弱解的存在唯一性

考虑了一类四阶非线性奇异抛物方程,给出了其变分问题,并证明了相应变分问题弱解的存在唯一性.