一类非线性扩散问题解的局部化

This paper concerns with properties of solutions of a nonlinear diffusion problem in non-divergence form.By constructing proper test functions,it is proved that solutions of the problem possess the property of localization.     

p-级数余项的一个估计

文献《On elementary bounds for ∑∞k=n 1/k^s》(American Mathematical Monthly,2015,122(2):155-158)给出了p-级数余项的一个估计,本文利用Taylor展开公式进一步改进了这个估计.     

关于一类非散度型非线性退化抛物方程的一些结果

In this paper, we are concerned with the initial and boundary value problem for the following equations not in divergence form:     

Existence and Nonuniqueness of Weak Solutions of the Initial-Boundary Value Problem for ut=u^σ div（｜△↓u｜^（p-2）△↓u）

In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut =u^σ div(|△↓u|^(p-2)△↓u) with σ≥1. Localization property of weak solutions is also discussed.     

一类奇异半线性椭圆方程解的不存在性

研究了一类奇异半线性椭圆方程解的不存在性,改进并补充了Arcoya等人的一个研究工作[Existence and nonexistence of solutions for singular quadratic quasilinear equations,J Differential Equations,2009,246:4006-4042].本文使用的方法非常简单,证明过程中用到了Poincare等式,Lusin定理以及Egoroff定理.     

一类非线性奇异椭圆方程的非平凡解

讨论一类非线性奇异椭圆方程边值问题,运用正则化方法,经过取两次极限,得到了这个问题的一个非平凡解.     

CAUCHY PROBLEM FOR A DEGENERATE PARABOLIC EQUATION WITH NON-DIVERGENCE FORM

In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form.     

具有接种的确定性和随机SIS流行病模型的全局稳定性

We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma(2004), for which some sufficient conditions for the global stability of the endemic equilibrium were given in some earlier works. In this paper, we first prove by Lyapunov function method that the endemic equilibrium of the deterministic model is globally asymptotically stable whenever the basic reproduction number is larger than one. For the stochastic version, we obtain some sufficient conditions for the global stability of the endemic equilibrium by constructing a class of different Lyapunov functions.     

一类奇异非线性扩散问题(英文)

In thisP即er，we are interested in the nonnegative solutions for the singular nonlinear di如sion Problem 、、..才尹 ﹃.上 . 11 了.‘、 (P)、 “。=”口(△，。 入。”一1 二(x，亡)=0 。(x，0)=二。(x) in几T， ona几x(0，T) in几， where几二=几x(o，T)，T>o，fl 1