一类含多奇性项的Grushin型算子方程解的渐近性质

本文研究了一类含多个奇性项的Grushin型算子方程非平凡解的渐近性质问题.当方程的非线性项满足临界指数增长条件时,利用Moser迭代方法和分析技巧,获得了方程的非平凡解在奇点处的渐近性质,推广了Laplace算子的相关结果.     

RN中含Φ-Laplace算子和凹凸非线性项的拟线性椭圆型方程解的存在性

该文研究了全空间中一类含Φ-Laplace算子和凹凸非线性项的拟线性椭圆型方程非平凡解的存在性和多重性.利用Nehari流形方法和纤维映射等技巧,在参数较小的情况下,得到方程至少有两个非平凡解,其中一个是基态解.     

具有无界非线性项的半线性椭圆共振问题

本文中我们研究一类在高阶特征值处共振、具有无界的非线性项的渐近线性椭圆方程的非平凡解的存在性．     

一个带Hardy项的椭圆方程的多重解

通过对偶变分方法证明了一个带Hardy项和临界非线性的非线性椭圆方程的非平凡解的存在性和多重性.     

一类带变号非线性项Dirac方程解的存在性

本文讨论一类具有周期性的非线性Dirac方程.在适当的条件下,当非线性项是超线性的并且变号时,利用变分方法得到Dirac方程至少有一个非平凡解.     

FitzHugh-Nagumo方程的分歧北大核心

运用非线性分歧理论,研究FitzHugh-Nagumo方程的定态分歧和Hopf分歧.证明了FitzHugh-Nagumo方程在适当条件下有定态分歧发生,此时FitzHugh-Nagumo方程的定态方程有非平凡解存在.另外还证明了FitzHugh-Nagumo方程在适当的条件下有Hopf分歧发生,此时该方程从平凡解分歧出非平凡的周期解.最后分析得出影响FitzHugh-Nagumo方程分歧发生的主要因素是离子电压门控通道打开与关闭的延迟反应的快慢.理论分析所得结果与实验现象是相一致的.     

一类含权的凹凸非线性Kirchhoff型方程解的多重性

本文在■中研究加权凹凸非线性Kirchhoff型方程,当非线性项中位势函数满足适当条件时,利用山路引理和Ekeland变分原理获得了两个非负非平凡解的存在性结果.     

奇异扰动的p-Laplace方程非负非平凡解和正解的结构

精确地刻画了某些奇异扰动的p-Laplace方程非负非平凡解和正解的结构．利用上下解方法证明，方程存在很多非负非平凡的尖峰解和正的过渡尖峰解．当参数充分小时还对每个尖峰解支集的上下界进行了估计．     

一类R~N上的半线性椭圆方程的多个非负解

本文研究一类R~N上带凸-凹非线性项的半线性椭圆方程,其中的非线性项含有可变号的权函数;通过运用变分方法中的大范围纤维方法,证明了当权函数和参数满足一定条件时方程存在两个非平凡的非负解.     

FitzHugh-Nagumo方程的分歧

运用非线性分歧理论,研究FitzHugh-Nagumo方程的定态分歧和Hopf分歧.证明了FitzHugh-Nagumo方程在适当条件下有定态分歧发生,此时FitzHugh-Nagumo方程的定态方程有非平凡解存在.另外还证明了FitzHugh-Nagumo方程在适当的条件下有Hopf分歧发生,此时该方程从平凡解分歧出非平凡的周期解.最后分析得出影响FitzHugh-Nagumo方程分歧发生的主要因素是离子电压门控通道打开与关闭的延迟反应的快慢.理论分析所得结果与实验现象是相一致的.     

Almost Periodic Solutions of Nonlinear Second Order Differential Equations

We provide existence results for almost periodic solutions of nonlinear second order ordinary differential equations. The results extend existence results for periodic solutions of periodic equations, where the existence of periodic sub and supersolutions implied the existence of periodic solutions.     

System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of the Debreu vector equilibrium problems and the Nash vector equilibrium problems.     

Variational inclusions problems with applications to Ekeland’s variational principle,fixed point and optimization problems

In this paper, we prove the existence theorems of two types of systems of variational inclusions problem. From these existence results, we establish Ekeland’s variational principle on topological vector space, existence theorems of common fixed point, existence theorems for the semi-infinite problems, mathematical programs with fixed points and equilibrium constraints, and vector mathematical programs with variational inclusions constraints.     

一类泛函微分方程半正问题的正周期解

运用Krasnosel’skii不动点理论研究了一类含参泛函微分方程半正问题正周期解的存在性．获得了当参数充分小时正周期解的存在性结果以及半正问题正周期解存在的充分条件．丰富了一阶泛函微分方程解的存在性理论．     

Traveling waves in delayed lattice dynamical systems with competition interactions

This paper deals with the existence of traveling wave solutions of a class of delayed system of lattice differential equations, which formulates the invasion process when two competitive species are invaders. Employing the comparison principle of competitive systems, a new cross-iteration scheme is given to establish the existence of traveling wave solutions. More precisely, by the cross-iteration, the existence of traveling wave solutions is reduced to the existence of an admissible pair of upper and lower solutions. To illustrate our main results, we prove the existence of traveling wave solutions in two delayed two-species competition systems with spatial discretization. Our results imply that the delay appeared in the interspecific competition terms do not affect the existence of traveling wave solutions.     

线性增长条件下一类非线性梁方程解的存在性

考察了一类非线性四阶两点边值问题的解的存在性.通过构造适当的Banach空间并且利用积分方程建立了一个存在定理.主要工具是Leray-Schauder非线性抉择.本文表明,如果非线性项在其定义域的某个有界子集上的增长速度是线性的,该问题可能存在解.     

Square of countably compact groups without non-trivial convergent sequences

We show in ZFC that the existence of a countably compact Abelian group without non-trivial convergent sequences implies the existence of a countably compact group whose square is not countably compact.This improves a result obtained by van Douwen in 1980: the existence of a countably compact Boolean group without non-trivial convergent sequences implies the existence of two countably compact groups whose product is not countably compact in ZFC.Hart and van Mill showed in 1991 the existence of a countably compact group whose square is not countably compact under Martin's Axiom for countable posets. We show that the existence of such an example does not depend on some form of Martin's Axiom.     

Existence of solutions of non-autonomous second order functional differential equations with infinite delay

In this paper the existence of solutions of a non-autonomous abstract retarded functional differential equation of second order with infinite delay is considered. Assuming the existence of an evolution operator corresponding to the associate abstract Cauchy problem of second order, we establish the existence of mild solutions of the functional equation. Furthermore, we study the existence of classical solutions of the abstract Cauchy problem of second order and we apply these results to establish the existence of classical solutions of the functional equation. Finally, we apply our results to study the existence of solutions of the non-autonomous wave equation with delay.     

Existence of equilibria for generalized games without paracompactness

In this paper, we first prove an existence theorem of maximal elements without any paracompactness. Then, we establish an existence theorem of equilibrium points of generalized games with infinite many players and without any paracompactness, by applying our maximal element existence theorem. Our equilibrium existence theorem answers the two questions raised by Kim [6] in the affirmative.     

一类混合型微分差分方程的周期解

利用Fenchel变换,我们推出一类微分差分方程存在周期解等价于某泛函具有临界点,并求出方程具有周期解的充分条件.