一类阻尼振动问题的周期解的存在性（英文）

本文致力于研究一类带阻尼问题周期解的存在性问题.借助于辅助函数,我们得到了一些新的超二次增长和渐进二次增长条件,利用临界点理论中的极大极小方法,获得一些新的存在性结果,推广了已有文献中相关存在性结论.     

一类次线性基尔霍夫方程解的存在性（英文）

本文研究一类不确定型的基尔霍夫方程.在线性泛函满足新的次线性增长条件和扰动势能合适的条件下,利用变分法得到该类方程的非平凡解的存在性.     

具无穷时滞非线性生态竞争系统的正周期解

讨论了一类无穷时滞非线性生态竞争系统的正周期解,利用变量变换和不动点定理,得到了该系统的正周期解的存在性和存在唯一性的充分性条件,获得了一些新的结果.     

一类超线性二阶Hamiltonian周期解的存在性（英文）

本文研究一类具新的超二次条件的二阶Hamiltonian系统周期解问题,利用同调环绕理论和Morse理论得到一些周期解的存在性结论.     

一类二阶哈密顿系统的周期解

本文考虑一类二阶哈密顿系统,利用临界点理论中的极小极大理论和局部环绕理论,在一类新的次二次增长条件下,研究得到了非平凡周期解的存在性.证明过程不依赖于经典的Palias-Smale紧性.     

2m阶Dirichlet边值问题的多解(英文)

本文讨论了非线性2m阶Dirichlet边值问题多解的存在性.在非线性项满足一定条件时,通过有效地利用锥中的不动点指数理论和解的反对称延拓法,得到关于变号解的一些新的存在结果.确切地说,得到该2m阶边值问题至少存在两个正解,两个负解和多个变号解.     

一类带阻尼项的次二次二阶Hamilton系统的周期解

本文研究了一类带阻尼项的二阶Hamilton系统周期解的存在性问题.利用鞍点定理,在新的次二次条件下,获得了一个新的存在性结果,推广并改进了已有文献的相关存在性结论.     

二阶非自治Hamilton 系统周期解的新结果

研究了二阶非自治Hamilton系统（t）-B（t）x（t）＋▽H（t,x（t））=0,在局部超二次条件下周期解的存在性问题,利用山路定理和局部环绕定理得到了新的存在性定理,改进了已有结果.     

带有R-S积分边值条件的分数阶朗之万方程的解的存在性

研究一类带有R-S积分边值条件的非线性分数阶朗之万方程边值问题.利用Leray-Schauder非线性抉择和Leray-Schauder度理论,得到几个新的存在性结果.最后给出一个例子来证明主要结论的应用性.     

时滞脉冲抛物型微分方程解的存在性及其在种群动力学中的应用

本文研究了一类具有时滞的脉冲抛物型方程在Neumann边值条件下解的存在性问题,利用定义上下解对的方法,给出了一个新的解的存在性定理和比较原理.作为例子,当把这种方法应用到一种群模型中时,得到了该系统正平衡点全局吸引的新结果.     

Necessary and sufficient conditions for the existence of shock curves of hyperbolic 1-conservation laws

We present three conditions for the existence of shock curves of hyperbolic 1-conservation laws. If at least two of the conditions hold, then shock curves exist uniquely in the classical sense. We present an example (Example 2, Section 4) for which two of the conditions do not hold and a new kind of singularity occurs. In Remark 1 we present two other conditions similar to the above three conditions which also imply the existence of shock curves.     

Traveling wave solutions in delayed reaction-diffusion systems with mixed monotonicity

This paper deals with the existence of traveling wave solutions in delayed reaction-diffusion systems with mixed monotonicity. Based on two different mixed-quasi monotonicity reaction terms, we propose new conditions on the reaction terms and new definitions of upper and lower solutions. By using Schauder’s fixed point theorem and a new cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained have been applied to type-K monotone and type-K competitive diffusive Lotka-Volterra systems.     

Matrices with prescribed characteristic polynomial and principal blocks. II

In this paper we present some new sufficient conditions for the existence of a square matrix with prescribed characteristic polynomial and two complementary principal submatrices.     

含一阶导数的二阶微分方程组m点边值问题正解的存在性

讨论了二阶带一阶导数的微分方程组m点边值问题正解的存在性,利用一个新的不动点定理,得到上述问题具有一个正解的充分条件.     

Positive solutions for a high-order semipositone fractional differential equation with integral boundary conditions

In this paper, we consider the existence of positive solutions for a high-order semipositone fractional differential equation with Riemann-Stieltjes integral boundary conditions. By Krasnoselskii-Zabreiko fixed point theorem and some inequalities associated with Green’s function, two new existence theorems are obtained in the case that the nonlinearity f is allowed to grow both superlinearly and sublinearly. Finally, two examples are given to illustrate the main results.     

Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization

We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz–John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new properties, pseudonormality and quasinormality, emerge as central within the taxonomy of interesting constraint characteristics. In the case where there is no abstract set constraint, these properties provide the connecting link between the classical constraint qualifications and two distinct pathways to the existence of Lagrange multipliers: one involving the notion of quasiregularity and the Farkas lemma, and the other involving the use of exact penalty functions. The second pathway also applies in the general case where there is an abstract set constraint.     

Saddle Points Theory of Two Classes of Augmented Lagrangians and Its Applications to Generalized Semi-infinite Programming

In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle points is that we do not need the uniqueness of the optimal solution. Furthermore, we show that the existence of global saddle points is a necessary and sufficient condition for the exact penalty representation in the framework of augmented Lagrangians. Based on these, we convert a class of generalized semi-infinite programming problems into standard semi-infinite programming problems via augmented Lagrangians. Some new first-order optimality conditions are also discussed. This research was supported by the National Natural Science Foundation of P.R. China (Grant No. 10571106 and No. 10701047).     

On the Existence of Large Sets of <Emphasis Type="Italic">t</Emphasis>-designs of Prime Sizes

In this paper, we employ the known recursive construction methods to obtain some new existence results for large sets of t-designs of prime sizes. We also present a new recursive construction which leads to more comprehensive theorems on large sets of sizes two and three. As an application, we show that for infinitely many values of block size, the trivial necessary conditions for the existence of large sets of 2-designs of size three are sufficient.AMS Classification: 05B05Communicated by:L. TeirlinckThis research was in part supported by a grant from IPM (No. 83050312).     

Bilevel Decision with Generalized Semi-infinite Optimization for Fuzzy Mappings as Lower Level Problems

In this paper, we introduce the bilevel decision problems with parametric generalized semi-infinite optimization for fuzzy mappings as the lower-level problem, and its corresponding MPEC problems. For these problems, we establish two models which are different in the feasible region setting of lower-level problems. Some new existence results are obtained in rather weak conditions.