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A GENERAL AVERAGING METHOD FOR AFFINE PERIODIC SOLUTIONS

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Acta Mathematica Scientia 2024年第6期44卷 2207-2224页

作者： Xue YANG Jiamin XING Yong LI College of Mathematics Jilin UniversityChangchun 130012China School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sci Northeast Normal UniversityChangchun 130024China

We consider the persistence of affine periodic solutions for perturbed affine periodic ***(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular *** are a kind of spatiotemporal symmetric solutions,*** *** give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic *** transversal condition is determined using the brouwer *** also present a higher order averaging method for general degenerate systems by means of the brouwer degree and a Lyapunov-Schmidt reduction.

关键词： affine-periodic solution perturbed system brouwer degree averaging method

Bolzano's Theorems for Holomorphic Mappings(To Ham Brezis,with friendship and admiration)

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Chinese Annals of Mathematics,Series B 2017年第2期38卷 563-578页

作者： Jean MAWHIN institut de recherche en mathématique et physique universitécatholique de louvain chemin du cyclotron2 1348 Louvain-la-NeuveBelgium

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions. A more complicated proof, using Cauchy's argument principle, provides uniqueness of the zero, when the sign conditions on the boundary are strict. Applications are given to corresponding brouwer fixed point theorems for holomorphic functions. Extensions to holomorphic mappings from C^n to C^n are obtained using brouwer degree.

关键词： Holomorphic function Hadamard-Shih's conditions Poincaré-Miranda's conditions Bolzano's theorem Cauchy's theorem brouwer fixed point theorem brouwer degree

THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS AT RESONANCE

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Applied Mathematics and Mechanics(English Edition) 2000年第11期21卷 1282-1291页

作者：马世旺王志成庾建设 Department of Applied Mathematics Shanghai Jiaotong University Shanghai 200030 P R China Depamnent of Applied Mathematics Hunan University Changsha 410082 P R China

The nonlinear system of first-order differential equations with a deviating argument

关键词： first-order differential equation periodic solution resonance brouwer degree coincidence degree Duffing equation

Existence of Solutions of a Two-Point Boundary Value Problem

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Acta Mathematicae Applicatae Sinica 2005年第1期21卷 77-80页

作者： Shu-hongWu DepartmentofMathematics HuazhongUniversityofScienceandTechnologyWuhan430074.China

A two-point boundary value problem with a non-negative parameter Q arising inthe study of surface tension induced flow of a liquid metal or semiconductor is studied. We provethat the problem has at least one solution ... 详细信息

关键词： two-point boundary value problem brouwer degree existence of solution 2000