一类非线性椭圆型方程的Dirichlet问题

本文讨论非线性椭圆型方程的Dirichlet问题．利用Schauder不动点定理及先验估计方法得到主要结果：存在正的光滑解．     

THREE-SPHERE INEQUALITIES FOR SECOND ORDER SINGULAR PARTIAL DIFFERENTIAL EQUATIONS

In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div(A▽u)-V u = 0, and the three-ball inequalities on the characteristic plane and the three-cylinder inequalities for the singular parabolic equation ■tu-div(A▽u)+ V u = 0, where the singular potential V belonging to the Kato-Fefferman- Phong’s class. Some applications are also discussed.     

On the Boundary Behaviour,Including Second Order Effects,of Solutions to Singular Elliptic Problems

For γ≥1 we consider the solution u=u（x） of the Dirichlet boundary value problem Δu ＋ u^-γ=0 in Ω, u=0 on δΩ. For γ= 1 we find the estimate u（x）=p（δ（x））[1＋A（x）（log 1/δ（x）^-6], where p（r） ≈ r r√2 log（1/r） near r = 0,δ（x） denotes the distance from x to δΩ, 0 〈ε 〈 1/2, and A（x） is a bounded function. For 1 〈 γ 〈 3 we find u（x）=（γ＋1/√2（γ-1）δ（x））^2/γ＋[1＋A（x）（δ（x））2γ-1/γ＋1] For γ3= we prove that u（x）=（2δ（x））^1/2[1＋A（x）δ（x）log 1/δ（x）]     

A ROBUST FINITE ELEMENT METHOD FOR A 3-D ELLIPTIC SINGULAR PERTURBATION PROBLEM

This paper proposes a robust finite element method for a three-dimensional fourth-order elliptic singular perturbation problem. The method uses the three-dimensional Morley element and replaces the finite element functions in the part of bilinear form corresponding to the second-order differential operator by a suitable approximation. To give such an approximation, a convergent nonconforming element for the second-order problem is constructed. It is shown that the method converges uniformly in the perturbation parameter.     

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.     

奇异半线性椭圆问题解的存在与不存在性(英文)

本文研究了奇异半线性椭圆问题.利用上下解方法,获得了该问题解的一个存在性和不存在性结果.     

一类奇异共振椭圆方程正解的唯一性

本文研究了一类奇异椭圆方程的共振问题.利用变分方法,获得了该问题正解的唯一性,推广了Pino~([3])的结果.     

加权奇异拟线性椭圆方程特征值问题

在加权Sobolev空间中,利用Galerkin方法及推广的Brouwer定理,研究一类奇异拟线性椭圆方程高阶特征问题,得到了其非平凡弱解的存在性.     

一类半线性椭圆型方程奇摄动Robin边值问题

The singularly perturbed Robin boundary value problems for the semilinear elliptic equation are considered. Under suitable conditions and by using the fixed point theorem the existence ,uniqueness and asymptotic behavior of solution for the boundary value problems are studied.     

临界增长的半线性椭圆方程的一个奇异扰动问题

本文考虑下面的奇异扰动问题－Δｕ＝ｕ２－１＋εｕ，ｘ∈Ω；ｕ＞０，ｘ∈Ω；ｕ＝０，ｘ∈Ω，其中Ω是ＲＮ的一个有界区域，Ｎ５，２＝２ＮＮ－２本文证明了当ｘ０是Ｈ（ｘ，ｘ）的一个严格局部极小点时，其中Ｈ（ｘ，ｙ）是Ｇｒｅｅｎ函数的正则部分，则所考虑的问题在ε＞０充分小时，存在解ｕε满足｜Ｄｕε｜２ＳＮ／２δｘ０，这里，Ｓ是Ｓｏｂｏｌｅｖ嵌入Ｈ１（ＲＮ）Ｌ２（ＲＮ）的最佳常数