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Existence of periodic points of endomorphisms of a circle

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Science China Mathematics 1999年第1期42卷 13-17页

作者：李伟固 Department of Mathematics Peking University Beijing China

A theorem of Block and Franke is improved on the existence of periodic points for a map of a circle to itself and a proof which seems more understandable is given.

关键词： endomorphism rotation set periodic point.

On the Quasi-periodic Wave Solutions and Asymptotic Analysis to a(3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

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Communications in Theoretical Physics 2014年第8期61卷 245-258页

作者：田守富马潘丽 Department of Mathematics China University of Mining and TechnologyXuzhou Center of Nonlinear Equations China University of Mining and TechnologyXuzhou

In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.

关键词： a(3+1)-dimensional generalized Kadomtsev–Petviashvili equation Bell’s polynomials Riemann theta function soliton solution periodic wave solution

Existence of almost periodic solutions of second order neutral delay differential equations with piecewise constant argument

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Science China Mathematics 1998年第3期41卷 232-241页

作者：袁荣 Department of Mathematics Beijing Normal University Beijing China

By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument d 2dt 2x(t)+px(t-1))=qx((... 详细信息

关键词： almost periodic solutions almost periodic sequences neutral delay equation piecewise constant argu-ment.

ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF periodic HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2010年第4期30卷 1291-1300页

作者：肖丽鹂陈宗煊 Institute of Mathematics and Informations Jiangxi Normal University School of Mathematical Science South China Normal University

In this article, the zeros of solutions of differential equation f^（k）（z）＋A（z）f（z） = 0, are studied, where k 2, A（z） = B（e^z）, B（ζ） = g1（1/ζ）＋ g2（ζ）, g1 and g2 being entire functions with g2 transcendental and σ（g2） not equal to a positive integer or infinity. It is shown that any linearly independent solutions f1, f2, . . . , fk of Eq.（＊） satisfy λe（f1 . . . fk） ≥ σ（g2） under the condition that fj（z） and fj（z＋ 2πi）（j = 1, . . . , k） are linearly dependent.

关键词： Differential equation periodic linearly dependent complex oscillation

Existence of almost periodic solutions of neutral differential equations with piecewise constant argument

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Science China Mathematics 1996年第11期39卷 1164-1177页

作者：袁荣洪佳林 Department of Mathematics Beijing Normal University Beijing 100875 China Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China

Based on the properties on almost periodic sequence, it is proved that the almost periodic solutions for a class of neutral differential equations with piecewise constant argument exist.

关键词： almost periodic solutions almost periodic sequences piecewise constant argument neutral differential equations.

Existence and global attractivity of a positive periodic solution of a class of delay differential equation

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Science China Mathematics 1998年第3期41卷 273-284页

作者：李永昆 Department of Mathematics Yunnan University Kunming China

The existence and the global attractivity of a positive periodic solution of the delay differential equation y·(t)=y(t)F[t, y(t-τ 1(t)),...,y(t-τ n(t))] are studied by using some techniques of the Mawhin coincidence degree theory and the constructing suitable Liapunov functionals. When these results are applied to some special delay bio-mathematics models, some new results are obtained, and many known results are improved.

关键词： delay differential equation logistic equation positive periodic solution global attractivity Fredholm mapping.

Exponential stability and periodic solutions of delayed cellular neural networks

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Science China(Technological Sciences) 2000年第3期43卷 328-336页

作者：曹进德 Department of Applied Mathematics Southeast University Nanjing 210096 China

A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many parameters qij* , rij* , qij, rij∈ R and wi>0 (i, j = 1, 2, …, n) and combining them with the elementary inequality 2ab≤a2 + b2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.

关键词： periodic solution global exponential stability delayed cellular neural networks Lyapunov func-tional inequality.

Multiple periodic Solutions of Differential Delay Equations with 2k-1 Lags

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Acta Mathematicae Applicatae Sinica 2020年第2期36卷 390-400页

作者： Lin LI Hua-fei SUN Wei-gao GE School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

In this paper,we study the periodic solutions to a type of differential delay equations with 2 k-1 lags.The 4 k-periodic solutions are obtained by using the variational method and the method of Kaplan-Yorke coupling system.This is a new type of differential delay equations compared with all the previous researches.And this paper provides a theoretical basis for the study of differential delay equations.An example is given to demonstrate our main results.

关键词： differential delay equation periodic solutions critical point theory variational method

Fifth-Order Alice-Bob Systems and Their Abundant periodic and Solitary Wave Solutions

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Communications in Theoretical Physics 2019年第10期71卷 1149-1154页

作者：赵启亮贾曼楼森岳 School of Physical Science and Technology Ningbo UniversityNingbo 315211China Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062China

The study on the nonlocal systems is one of the hot topics in nonlinear science. In this paper, the well-known fifth-order integrable systems including the Sawada-Kotera(SK) equation, the Kaup-Kupershmidt(KK) equation and the fifth-order Koterweg-de Vrise(FOKd V) equation are extended to a generalized two-place nonlocal form, the generalised fifth-order Alice-Bob system. The Lax integrability of two sets of Alice-Bob systems for all the SK, KK and FOKd V type systems are explicitly given via matrix Lax pairs. The ■ symmetry breaking and symmetry invariant periodic and solitary waves for one set of nonlocal SK, KK and FOKd V system are investigated via a special travelling wave solution ansatz.

关键词： Alice-Bob SK equarions Alice-Bob KK equations periodic and solitary waves