一类P—Laplace方程正解的存在性

本文在不满足(AR)条件下,利用山路引理,证明了P-Laplace方程Dirichlet问题正解的存在性.     

Schwarz引理的推广及其应用

引入Schwarz引理的一个最常见的推广定理,并且作出了详细的证明.同时以引理形式介绍了一个实用的复数性质,并且利用这两个引理,给出了开圆盘内解析函数的的实部,虚部以及模的估计式.     

李超代数的Schur引理

对经典文献中李超代数的Schur引理的各种表述进行比对研究.给出李超代数的Schur引理的明晰表达及证明;作为应用,刻画了一类Heisenberg李超代数的不可约模的自同态.进而利用奇偶函子和符号映射刻画了李超代数模同态的各种定义之间的关系.     

Memory estimation of inverse operators

We use methods of harmonic analysis and group representation theory to estimate the memory decay of the inverse operators in Banach spaces. The memory of the operators is defined using the notion of the Beurling spectrum. We obtain a general continuous non-commutative version of the celebrated Wiener's Tauberian Lemma with estimates of the “Fourier coefficients” of inverse operators. In particular, we generalize various estimates of the elements of the inverse matrices. The results are illustrated with a variety of examples including integral and integro-differential operators.     

ON CRITICAL SINGULAR QUASILINEAR ELLIPTIC PROBLEM WHEN n = p

This article deals with the problem where n = p. The authors prove that a Hardy inequality and the constant (p/p-1)p is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma.     

Automorphisms of Maps with a Given Underlying Graph and Their Application to Enumeration

A graph is called a semi-regular graph if its automorphism group action on its ordered pair of adjacent vertices is semi-regular. In this paper, a necessary and sufficient condition for an automorphism of the graph F to be an automorphism of a map with the underlying graph F is obtained. Using this result, all orientation-preserving automorphisms of maps on surfaces (orientable and non-orientable) or just orientable surfaces with a given underlying semi-regular graph F are determined. Formulas for the numbers of non-equivalent embeddings of this kind of graphs on surfaces (orientable, non-orientable or both) are established, and especially, the non-equivalent embeddings of circulant graphs of a prime order on orientable, non-orientable and general surfaces are enumerated.     

On 4-manifolds homotopy equivalent to surface bundles over surfaces

We show that a closed 4-manifold is homotopy equivalent to the total space of a surface bundle over a surface if the obviously necessary conditions on the fundamental group and Euler characteristic hold. When the base is the 2-sphere we need also conditions on the characteristic classes of the manifold. (Our results are incomplete when the base is the projective plane.) In most cases we can show the manifold is s-cobordant to the total space of the bundle.