泛函极小与椭圆型方程组解的正则性

研究定义在向量u=(u~1,…,u~N):Ω■R~n→R~N上的各项异性积分泛函F(u)=∫_Ωf(x,Du(x))dx和非线性椭圆型方程组-Σi=1nDi(aiα(x,Du(x)))=-Σi=1nDiFiα(x),α=1,2,…,N.在密度函数f:Ω×R~(N×n)→R和矩阵a=(a_i~α):Ω×R~(N×n)→R~(N×n)满足某单调不等式条件下,得到u整体有界.     

环域上一类二阶非线性椭圆系统的正对径解

研究环域上一类非线性二阶椭圆系统的正对径解的存在性和多解性，章的主要思想是锥拉伸与锥压缩型的Krasnosel’skii不动点定理的局部应用。     

临界增长的椭圆型方程广义解的有界性及先验估计

本文证明了椭圆型方程由divA（x,u,u）=B(x,u,u)(在G内)在带权soblev空间中的广义解的有界性,并做出了有界解最大模的先验估计．A（x,u,ζ)和B（x,u,ζ)关于u的增长阶达到了临界指数,而且允许B（x,u,ζ)关于ζ的增长阶γ满足自然增长条件,从而推广和改进了已有的所有结果．     

ON ASYMPTOTIC CRITERIA FOR A SECOND ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper, we present some new asymptotic results for a second order elliptic differential equations by using integral averaging and completing square technique.     

POSITIVE SOLUTIONS AND BIFURCATION OF FULLY NONLINEAR ELLIPTIC EQUATIONS INVOLVING SUPER－CRITICAL SOBOLEV EXPONENTS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＯＦＦＵＬＬＹＮＯＮＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＩＮＶＯＬＶＩＮＧＳＵＰＥＲ－ＣＲＩＴＩＣＡＬＳＯＢＯＬＥＶＥＸＰＯＮＥＮＴＳ￥ＱＵＣＨＡＮＧＺＨＥＮＧ（屈长征）（Ｉｎｓ...     

Strong Solution of the Obstacle Problem for Fully Nonlinear Elliptic Equations

In this paper we obtain the existence of W^{2, ∞} solutions of the obstacle problems for fully nonlinear elliptic equations under more general structure conditions than those in [1] by using the mollifier approach, which is also extended in our discussion.     

Morrey Regularity of Solutions to Degenerate Elliptic Equations in Rn

In this paper, we study the Morrey regularity of solutions to the de- generate elliptic equation -(a_{ij}u_{xi})_{xj} = -(f_j)_{xj} in R^n. For this purpose, we introduce four weighted Morrey spaces in R^n.     

Existence and Regularity of Solutions of a Nonlinear Nonuniformly Elliptic System Arising from a Thermistor Problem

A thermistor is an electric circuit device made of ceramic material whose electric conductivity depends on the temperature. If the only heat source is the electric heating, the temperature and the electric potential satisfy a nonlinear elliptic system which is also degenerate if the electric conductivity is not uniformly bounded from above or away from zero. Under general boundary conditions, we establish existence and Hölder continuity of solutions of such a nonlinear nonuniformly elliptic system. When the elechic conductivity linearly depends on the temperature, we provide a non-uniqueness and non-existence example.     

Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems

We show that entire positive solutions exist for the semilinear elliptic system Δu = p(x)v^α, Δv = q(x)u^β on R^N, N ≥ 3, for positive α and β, provided that the nonnegative functions p and q are continuous and satisfy appropriate decay conditions at infinity. We also show that entire solutions fail to exist if the functions p and q are of slow decay.     

退化的非线性椭圆方程的径向解

利用打靶法讨论一类退化非线性椭圆型方程径向解的性态，得出了径向解的间断及不间断的结果．     

A remark on the existence of entire large and bounded solutions to a (<Emphasis Type="Italic">k</Emphasis><Subscript>1</Subscript>, <Emphasis Type="Italic">k</Emphasis><Subscript>2</Subscript>)-Hessian system with gradient term

In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system

$$\left\{ {\begin{array}{*{20}c}{S_{k_1 } \left( {\lambda \left( {D^2 u_1 } \right)} \right) + a_1 \left( {\left| x \right|} \right)\left| {\nabla u_1 } \right|^{k_1 } = p_1 \left( {\left| x \right|} \right)f_1 \left( {u_2 } \right)} & {for x \in \mathbb{R}^N ,} \\{S_{k_2 } \left( {\lambda \left( {D^2 u_2 } \right)} \right) + a_2 \left( {\left| x \right|} \right)\left| {\nabla u_2 } \right|^{k_2 } = p_2 \left( {\left| x \right|} \right)f_2 \left( {u_1 } \right)} & {for x \in \mathbb{R}^N .} \\\end{array} } \right.$$

Here \({S_{{k_i}}}\left( {\lambda \left( {{D^2}{u_i}} \right)} \right)\) is the k _i -Hessian operator, a ₁, p ₁, f ₁, a ₂, p ₂ and f ₂ are continuous functions.

     

A necessary and sufficient condition for the existence of large solutions to sublinear elliptic systems

We prove that the elliptic system Δu=p(|x|)vα, Δv=q(|x|)uβ on Rn (n?3) where 0<α?1, 0<β?1, and p and q are nonnegative continuous functions has a nonnegative entire radial solution satisfying lim|x|→∞u(x)=lim|x|→∞v(x)=∞ if and only if the functions p and q satisfy

     

一类四阶非线性椭圆问题变号解的存在性

通过建立一个新空间,在新空间中讨论了一个含Hardy位势的四阶非线性椭圆问题变号解的存在性.在一个环绕定理下,得到了问题变号解的存在性.