具有饱和恢复率的SEIR时滞模型的行波解

研究一类具有饱和恢复率的SEIR时滞模型的行波解.首先,考虑一类二维系统初值问题的适定性;然后,通过构造一对有界的向量值上、下解得到一个闭凸集;最后,利用Schauder不动点定理证明:当基本再生数R^(0)>1,波速c>c^(*)时模型存在非平凡行波解.

具有时空时滞的非局部扩散SIR模型的行波解

针对种群中的染病个体在疾病潜伏期内具有自由移动和传染疾病的现象,研究了一个具有时空时滞的非局部扩散SIR模型的行波解问题.利用基本再生数和最小波速判定行波解是否存在.首先,通过在有界区域上构造一个初始函数的不变锥,利用Schauder不动点定理证明在该锥上存在不动点,然后通过取极限的方法得到行波解的存在性.其次,利用双边Laplace(拉普拉斯)变换法证明了行波解的不存在性.由于行波解的最小传播速度对控制疾病传播具有重要的指导意义,最后讨论了非局部扩散、时滞等因素对最小波速的影响.

Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .

A QUASILINEAR SINGULAR ELLIPTIC SYSTEM WITHOUT COOPERATIVE STRUCTURE

In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.

Traveling Wavefronts on Reaction Diffusion Systems with Spatio-Temporal Delays

By using Schauder’s Fixed Point Theorem, we study the existence of traveling wave fronts for reaction-diffusion systems with spatio-temporal delays. In our results, we reduce the existence of traveling wave fronts to the existence of an admissible pair of upper solution and lower solution which are much easier to construct in practice.

Existence and Uniqueness of Anti-periodic Solutions for 2n-order Differential Equations

In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.

ON THE STRICTLY POSITIVE SOLUTIONS OF NONAUTONOMOUS KOLMOGOROV COMPETITION SYSTEMS

In this paper, the existence of strictly positive solutions for N-species nonau- tonom ous Kolm ogorov com petition system s is studied. By applying the Schauder's fixed point theorem som e new sufficient conditions are established. In particular, for the alm ost periodic system , the existence of strictly positive alm ostperiodic solutions is obtained. Som e previous results are im proved and generalized.

Positive Solutions for Singular Boundary Value Problems of Coupled Systems of Nonlinear Differential Equations

We establish the existence of positive solutions for singular boundary value problems of coupled systems? The proof relies on Schauder’s fixed point theorem. Some recent results in the literature are generalized and improved.

Existence of Solutions for Some <i>p</i>(<i>x</i>)-polyharmonic Elliptic Kirchhoff Equations

In this paper, we study the existence of solution for some p(x)-polyharmonic Kirchhoff equations. The latter is allowed to vanish at the origin (degenerate case). Firstly, we study the existence of solutions of approximate equations. Secondly, we prove the existence of the solutions of the original equation. The main tool is the Schauder’s Theorem.

Existence of Traveling Waves in Lattice Dynamical Systems

Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c*>0 such that for each c≥c*, the systems under consideration admit monotonic nondecreasing traveling waves.

一类无穷域上高分数阶微分方程正解的存在性

为了研究无穷域上高分数阶微分方程多点边值问题正解的存在性,采用Schauder不动点定理及抉择定理,给出一类无穷域上高分数阶微分方程正解的存在条件以及迭代解,对分数阶微分方程解的存在性问题进行向高阶的推广.

Liénard型方程周期解的存在性

利用Sobolev空间范数,给出了一般形式的Liénard型方程周期解估计,通过Schauder不动点定理,证明了周期解的存在性。

一阶奇异耦合方程组周期边值问题的解(英文)

研究一阶奇异半正耦合微分方程组周期边值问题.对该方程组不同的半正形式,建立半正耦合方程组周期边值问题解的存在性的充分条件,定理的证明依赖于Schauder不动点定理。

一类具p-Laplace算子边值问题解的存在性

研究一类具p-Laplace算子的微分方程四点边值问题解的存在性.通过一个形式参数,将该问题间接地转化为一个等价的积分算子不动点问题.在非线性项有界、无界以及局部有界条件下,利用Schauder不动点定理分别得到了边值问题解存在的充分条件.

一类四阶奇边值问题的可解性

运用Ｓｃｈａｕｄｅｒ不动点定理研究了四阶两点边值问题ｄ４ｙｄｘ４＝ ｈ（ｘ）Ｆ（ｘ，ｙ（ｘ））（０＜ ｘ＜ １），ｙ（０）＝ ｙ（１）＝ ｙ″（０）＝ ｙ″（１）＝ ０ 的可解性，允许Ｆ（ｘ，ｙ）在ｘ＝ ０，ｘ＝ １ 或ｙ＝ ０。

一类积分微分包含的可控体

研究了一类带有非局部条件积分微分包含的可控性,在多值函数F(t,x)取凸和非凸两种情形下讨论了上述问题,建立了可控性的充分条件．对于凸情形,将所讨论的问题转化为集值积分算子的不动点问题,利用Kakutani不动点定理得到可控性．对于非凸情形,将所讨论的问题转化为单值积分算子的不动点问题,利用Schauder不动点定理得到可控性．

带弱奇异项的二阶微分方程正周期解的存在性（英文）

本文运用Schauder不动点定理获得了一类二阶非线性微分方程u″+a(t)u=f(t,u)+c(t)正周期解的存在性,其中a∈L^1(R/TZ;R+),c∈L^1(R/TZ;R),f为Carathéodory函数.本文的主要结果推广了一些已有结果.

非线性一阶常微分方程解的存在惟一性

讨论了一类非线性一阶常微分方程边值问题解的存在惟一性.得到了当参数在一定的范围取值时解存在惟一的充分条件,并包含了一些已知结果.主要结果基于Leray-Schauder非线性抉择理论和Banach不动点定理.

非线性薛定谔方程混合边界问题时间周期解的存在性

研究多维非线性薛定谔方程混合边界问题的时间周期解的存在性.首先利用Leray-Schauder不动点原理证明Galerkin近似问题有时间周期解,然后利用先验估计和紧致性证明近似解是收敛的,并且其极限就是原来问题的时间周期解.

一类无穷域上分数阶微分方程正解存在性

针对无穷域上非线性半正高阶分数阶微分方程多点边值问题正解的存在问题,采用Schauder不动点定理以及迭代的方法,研究该方程正解的存在性,给出了正解的存在条件.结果表明:对于无穷域上非线性半正高阶分数阶微分方程多点边值问题正解的存在性的证明,不需要使用复杂的对角化过程,即可得出结论,方法比以往更一般化、简单化.