Existence result for a gradient-type elliptic system involving a pair of p(x) and q(x)-Laplacian operators

In this paper, we deal with a typical gradient elliptic system involving a pair of p(x) and q(x)-Laplacian operators. Furthermore, the system may have nonlinearities with sign-changing. Precisely, we are interested in seeking at least one weak nontrivial solution. In this way, we establish explicitly a pair of lower and upper solutions having radial forms and related to the system. By applying the theory of monotone operators, we show that the system possesses at least one non-trivial and bounded solution.     

对称本原矩阵指数集的刻画

设Ｓｎ表示由全体ｎ阶对称本原（０，１）－矩所构成的集合，并设Ｓ（ｎ，ｄ）＝｛Ａ∈Ｓｎ│Ａ的伴随有向图中的最小奇圈之长为ｄ≥１｝。本文证明了：Ｓ（ｎ，ｄ）的本原指数集为｛ｄ－１，ｄ，…，２ｎ－ｄ－１｝＼Ｄ，其中Ｄ为｛ｎ－ｄ＋１，ｎ－ｄ＋２，…，２ｎ－ｄ－２｝中的所有奇数与０之并集，同时，我们也给出了Ｓ（ｎ，ｄ）中指数达到上界的矩阵集合的完全刻画。     

Higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients

In this paper, based on the theory of variable exponent spaces, we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain a local gradient estimate in Orlicz space for weak solution.     

On Coron's problem for the p-Laplacian

We prove that the critical problem for the p-Laplacian operator admits a nontrivial solution in annular shaped domains with sufficiently small inner hole. This extends Coron's result [4] to a class of quasilinear problems.     

Dirichlet零边值问题的正解存在性

由于一些本质困难,N=3被称为具Sobolev临界指数2*的Dirichlet问题-△u=λu+|u|2*-2u,x∈ΩRN;u(x)0,x∈Ω;u=0,x∈Ω的临界维数.众所周知,N=3时,上述问题存在古典(正)解的一个充分条件是Ω为R3上的小球以及14λ1λλ1.本文考虑Ω是R3中更一般的有界光滑区域,得出了一正解存在性结论,从而肯定了沈尧天在文中提及的一个未解决的问题.     

Strong regularizing effect of a gradient term in the heat equation with the Hardy potential

We deal with the following parabolic problem,

     

Multilinear Calderón-Zygmund Operators and Their Commutators with BMO Functions in Herz-Morrey Spaces with Variable Smoothness and Integrability

In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.     

一类含有奇数个顶点的三色有向图本原指数上界

一个三色有向图D是本原的,当且仅当存在非负整数h、k和v,且h+k+v0,使得D中的每一对顶点(i,j)都存在从i到j的(h,k,v)-途径,h+k+v的最小值定义为三色有向图D的本原指数.研究了一类三色有向图,它的未着色图中包含2佗-4个顶点,一个n-圈、一个(n-2)-圈和一个2-圈,给出了本原指数上界.     

Elliptic systems involving multiple strongly coupled critical terms

In this work, a singular elliptic system is investigated, which involves multiple strongly coupled critical terms. By means of variational methods and analytic techniques, the existence of positive solutions to the system is established.     

变指数Herz-Besov-Triebel空间的刻画

建立了变指数的Herz型Besov和Triebel-Lizorkin空间的离散刻画并利用此刻画得到了拟微分算子在这些空问上的有界性.