具有未知增长率的非线性系统的一般适应控制

阐明对于一类不确定系统在适当的条件下如何设计适应输出反馈控制器.这个不确定性来源于系统的未知参数.设计了一般输出反馈控制器结合Barbalat's引理从而证明系统的所有状态全局稳定.     

Remarks on homoclinic solutions for semilinear fourth-order ordinary differential equations without periodicity

This paper mainly discusses the existence of nontrivial homoclinic solutions for nonperiodic semilinear fourth-order ordinary differential equation
u^（4）＋pu″＋a（x）u-b（x）u^2=c（x）u^3=3
arising in the study of pattern formation by means of Mountain Pass Lemma.     

A note on kernels and Sperner’s Lemma

The kernel-solvability of perfect graphs was first proved by Boros and Gurvich, and later Aharoni and Holzman gave a shorter proof. Both proofs were based on Scarf’s Lemma. In this note we show that a very simple proof can be given using a polyhedral version of Sperner’s Lemma. In addition, we extend the Boros–Gurvich theorem to h-perfect graphs and to a more general setting.     

A Note on $Card(X)$

The main interests here are to study the relationship between $card(X)$ and $card({\cal P}(X))$ and the connection between the separability of a space $X$ and cardinality of some function space on it. We will convert the calculation of $card({\cal P}(X))$ to the calculation of $card({\cal F}(X\rightarrow Q))$.The main tool we used here is Zorn Lemma.     

带临界指数传输问题解的存在性研究

本文通过变分方法推广一类带权函数和临界指数的传输问题,先利用对称山路引理获得次临界情形无穷多解的存在性,再利用山路引理得到临界情形有限个正解的存在性.     

一类二阶哈密尔顿系统的周期解

在(CPS)_C及(PS)_C条件下,利用Ambrosetti-Rabinowitz对称形式的山路引理,研究了一类二阶哈密尔顿保守系统在给定能量面上的无穷多个周期解的存在性问题.     

How to avoid using the Regularity Lemma: Pósa’s conjecture revisited

In this paper we investigate how the use of the Regularity Lemma and the Blow-up Lemma can be avoided in certain extremal problems of dense graphs. We present the ideas for the following well-known Pósa conjecture on the square of a Hamiltonian cycle. In 1962 Pósa conjectured that any graph G of order n and minimum degree at least contains the square of a Hamiltonian cycle. In an earlier paper we proved this conjecture with the use of the Regularity Lemma-Blow-up Lemma method for n≥n₀ where n₀ is very large. Here we present another proof (and a general method) that avoids the use of the Regularity Lemma and thus the resulting n₀ is much smaller.     

退缩拟线性椭圆型方程某类边值问题的无穷多解

文[1]证明了如下D氏问题 -D_i(g|Du|~2)D_iu=f(x,u),x∈Ω, u=0,x∈Ω存在非平凡解,本文讨论上述方程的另一类边界问题 -D_i(g|Du|~2)D_iu=f(x,u),x∈Ω, g(|Du|~2)D_iu(0)(n,x_i)+h(x,u)=0,x∈Ω, (1)其中Ω∈R~n是具有光滑边界的有界区域,n(x)是Ω在x点的外法向,D_iu=u/x_i,Du=gradu=u,重复指标表示求和,与问题(1)相应的泛函为: