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特别的Manásevich-Mawhin连续定理及应用 被引量:1
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作者 周凯 周英告 《数学理论与应用》 2020年第1期19-33,共15页
在运用拓扑度的连续定理时,避免拓扑度的计算也就意味着最大化简化实际问题的处理过程.本文首先给出了一个特别的Manásevich-Mawhin连续定理和几个推论.相对于经典的Manásevich-Mawhin连续定理,在使用这个特别的连续定理及其... 在运用拓扑度的连续定理时,避免拓扑度的计算也就意味着最大化简化实际问题的处理过程.本文首先给出了一个特别的Manásevich-Mawhin连续定理和几个推论.相对于经典的Manásevich-Mawhin连续定理,在使用这个特别的连续定理及其推论处理实际问题时,我们能够避免计算拓扑度,且可以减少定理使用的条件.更重要的是,验证这个特别的连续定理的条件将更加容易和方便.其次,作为一个应用,本文应用上述特别的Manásevich-Mawhin连续定理研究了一般形式的Rayleigh型p-Lalacian泛函微分方程周期解和正周期解的存在性问题,获得了一些新的充分条件并推广和改进了一些已有的结果. 展开更多
关键词 拓扑度 Manásevich-mawhin连续定理 Rayleigh型p-Laplacian方程 周期解 正周期解
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ON THE CONDITIONAL VERSION OFKOLMOGOROV'S THREE-SERIES THEOREM 被引量:1
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作者 刘国欣 《Acta Mathematica Scientia》 SCIE CSCD 1999年第3期300-306,共7页
This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the con... This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained. 展开更多
关键词 Three-series theorem dependent r.v. s predictable local absolute continuITY MARTINGALE
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NASH EQUILIBRIA WITHOUT CONTINUITY OF THE CHOICE RULES
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作者 José C. R. Alcantud 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1535-1540,共6页
The proposal in Alcantud and Alo′s-Ferrer [1], where players that express their tastes according to choice rules facing a competitive situation, is further exploited here. We prove that, under lack of continuity of t... The proposal in Alcantud and Alo′s-Ferrer [1], where players that express their tastes according to choice rules facing a competitive situation, is further exploited here. We prove that, under lack of continuity of the choice rules it is also possible to ensure the existence of equilibrium. We shall appeal to general situations that are fulfilled by well-established models, where players have non-transitive preferences of various types. 展开更多
关键词 Nash equilibrium choice rules continuITY Kakutani’s theorem
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Framing Noether’s Theorem
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作者 Caesar P. Viazminsky 《Applied Mathematics》 2018年第3期274-286,共13页
We discuss Noether’s theorem from a new perspective and show that the spatial continuous symmetries of a system are on one hand symmetries of the space and on the other hand are dictated by the system’s potential en... We discuss Noether’s theorem from a new perspective and show that the spatial continuous symmetries of a system are on one hand symmetries of the space and on the other hand are dictated by the system’s potential energy. The Noether’s charges arising from an infinitesimal motion, or a Killing vector field, of the space, are conserved if the Lie derivative of the potential energy by this vector field vanishes. The possible spatial symmetries of a mechanical system are listed according to the potential energy of the external forces. 展开更多
关键词 Noether’s theorem continuous sPATIAL sYMMETRIEs CONsERVED MOMENTA
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Rothe’s Fixed Point Theorem and the Controllability of the Benjamin-Bona-Mahony Equation with Impulses and Delay
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作者 Hugo Leiva Jose L. Sanchez 《Applied Mathematics》 2016年第15期1748-1764,共18页
For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbation... For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions. 展开更多
关键词 Interior Approximate Controllability Benjamin Bona-Mohany Equation with Impulses and Delay strongly continuous semigroup Rothe’s Fixed Point theorem
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Generalized S-KKM Theorems and Minimax Inequalities in FC-Spaces
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作者 张红玲 范翠丽 《Journal of Southwest Jiaotong University(English Edition)》 2008年第3期303-307,共5页
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t... The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value. 展开更多
关键词 Generalized s-KKM type theorem Finitely continuous topological space FC-closed value Minimax inequalities
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S-R分解定理的张量表述及其率形式
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作者 谷凡 黄承逵 +1 位作者 李林普 周晶 《沈阳建筑大学学报(自然科学版)》 CAS 北大核心 2009年第1期6-11,共6页
目的研究S-R分解定理导出的应变率及旋转率,进一步完善S-R理论.方法以实方阵的对称、正交和分裂定理为基础,推导大变形、大转动情况下连续介质变形梯度张量的S-R分解定理,结合张量理论研究参数sinθ的本质及其在非笛卡尔坐标系下的计算... 目的研究S-R分解定理导出的应变率及旋转率,进一步完善S-R理论.方法以实方阵的对称、正交和分裂定理为基础,推导大变形、大转动情况下连续介质变形梯度张量的S-R分解定理,结合张量理论研究参数sinθ的本质及其在非笛卡尔坐标系下的计算公式,利用连续介质力学分析S-R分解定理前提条件、几何意义及由S-R分解定理导出的应变率和旋转率.结果由S-R分解定理导出的应变率、旋转率与通常使用的应变率、旋转率线性部分相同.结论将参数sinθ以张量形式表达可使S-R分解定理应用于非笛卡尔坐标系,同时需严格满足其前提条件.S-R理论体现了工程线应变、工程剪应变对应变张量S和局部刚体转动张量R的共同依赖性. 展开更多
关键词 实方阵 和分裂 连续介质 变形梯度张量 s—R分解定理 应变率 旋转率
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二阶非线性中立型泛函微分方程的周期解
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作者 倪晋龙 《科学技术创新》 2024年第20期31-34,共4页
本文利用Mawhin连续定理,研究了一类二阶非线性中立型时滞微分方程周期解的存在性,并给出了周期解存在的充分条件。
关键词 中立型微分方程 mawhin连续定理 周期解
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HOMOCLINIC SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS 被引量:2
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作者 鲁世平 郑亮 陈丽娟 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1361-1374,共14页
By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, ... By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set. 展开更多
关键词 homoclinic solution periodic solution neutral functional differential system mawhin's continuation theorem
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Existence of Solutions to Multi-point BVP with p-Laplacian at Resonance 被引量:2
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作者 LI Li-fang GE Wei-gao 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第3期379-384,共6页
This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),... This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance{(Φp (x'))' + f(t,x)=0,0 < t < 1,x' (0)=x'(ξ) x(1)=m-3 ∑i=1 βi x(η i),where βi∈ R,m-3 ∑i=1 β i=1,0 < η 1 < η 2 < ··· < ηm-3 < 1,m-3 ∑i=1 βiηi=1,0 < ξ < 1.An existence theorem is obtained by using the extension of Mawhin's continuation theorem.Since almost all the multi-point boundary value problem at resonance in previous papers are for the linear operator without p-Laplacian by the use of Mawhin's continuation theorem,our method is new. 展开更多
关键词 multi-point boundary value problem the extension of mawhins continuation theorem REsONANCE p-Laplacian operator
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Periodic Solutions of Mixed Type p-Laplacian Equations with Deviating Arguments 被引量:5
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作者 WANG Xiao-ming 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第2期177-182,共6页
Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,... Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results. 展开更多
关键词 P-LAPLACIAN periodic solutions mixed type deviating argument Man’asevichmawhin continuation theorem
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Existence of Solutions for Second Order Three-Point Boundary Value Problems with Nonlinear Growth 被引量:2
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作者 ZHANGHui-xing LIUWen-bin ZHANGJian-jun CHENTai-yong 《Journal of China University of Mining and Technology》 EI 2005年第2期163-166,共4页
The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have o... The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have one solution in c1[0,1] 展开更多
关键词 three-point boundary value problems REsONANCE mawhin continuation theorem.
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Periodic Solution of n-Species Gilpin-Ayala Competition System with Impulsive Perturbations 被引量:1
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作者 Kaihua Wang Zhanji Gui 《Journal of Software Engineering and Applications》 2012年第12期26-29,共4页
The principle aim of this paper is to explore the existence of periodic solution of n-Species Gilpin-Ayala competition system with impulsive perturbations. Sufficient and realistic conditions are obtained by using Maw... The principle aim of this paper is to explore the existence of periodic solution of n-Species Gilpin-Ayala competition system with impulsive perturbations. Sufficient and realistic conditions are obtained by using Mawhin's continuation theorem of the coincidence degree. Further, some numerical simulations show that our model can occur in many forms of complexities including periodic oscillation and chaotic strange attractor. 展开更多
关键词 Periodic solution IMPULsIVE PERTURBATIONs mawhins continuATION theorem
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SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY
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作者 孔凡超 罗治国 《Acta Mathematica Scientia》 SCIE CSCD 2017年第6期1803-1816,共14页
This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient co... This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results. 展开更多
关键词 solitary wave periodic wave mawhin's continuation theorem time:varyingdelay nonlinear sources
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Existence of Periodic Solutions for an Output Hidden Feedback Elman Neural Network
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作者 Valéry Covachev Zlatinka Covacheva 《Journal of Software Engineering and Applications》 2020年第12期348-363,共16页
<div style="text-align:justify;"> <span style="font-family:Verdana;">We first recall the sufficient conditions for the existence of a periodic output of a modified Elman neural network ... <div style="text-align:justify;"> <span style="font-family:Verdana;">We first recall the sufficient conditions for the existence of a periodic output of a modified Elman neural network with a periodic input found by using Mawhin’s continuation theorem of coincidence degree theory. Using this result, we obtain sufficient conditions for the existence of a periodic output for an output hidden feedback Elman neural network with a periodic input. Examples illustrating these sufficient conditions are given.</span> </div> 展开更多
关键词 Elman Neural Network Periodic Input and Output mawhins continuation theorem
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Comparison between Lambert and Maxwell Approaches in the Modelling of Microwave Heating of Liquid Foods
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作者 Rino Apicella Vittorio Romano 《Engineering(科研)》 2019年第1期1-13,共13页
Microwave heating of liquid foods in laminar flow through a circular tube has been modeled. In particular, skim milk as a Newtonian fluid and apple sauce and tomato sauce as non-Newtonian fluids have been considered. ... Microwave heating of liquid foods in laminar flow through a circular tube has been modeled. In particular, skim milk as a Newtonian fluid and apple sauce and tomato sauce as non-Newtonian fluids have been considered. The temperature profiles have been obtained solving the motion and energy equations in transient regime and Maxwell’s equations in the frequency domain. Numerical resolution of Finite Element Method has been implemented in Comsol Multiphysics. The generation term due to the microwave heating has been evaluated according both to Lambert’s law and Poynting theorem. Finally, a comparison between the two methods has been made in order to check to what extent the results obtained with the simpler Lambert’s law approximation are comparable with those deriving from the exact solution of Maxwell equations. Dielectric properties are considered to be temperature dependent. 展开更多
关键词 continuous Microwave HEATING Lambert’s LAW MAXWELL EQUATIONs Poynting theorem Non-Newtonian FLUIDs FEM
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3-PERIODIC ORBIT IMPLYING 683172687698650885-PERIODIC ORBITS——INFIMUMS OF NUMBERS OF PERIODIC ORBITS IN CONTINUOUS FUNCTIONS
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作者 麦结华 《Science China Mathematics》 SCIE 1991年第10期1194-1204,共11页
For any continuous function f on the interval I=[0, 1] and any m, n≥1, let N(n, f)denote the number of n-periodic orbits in f. Put N(n, m)=min{N(n, f):f is a continuousfunction on I, and N(m, f)≥1}. The famous Sarko... For any continuous function f on the interval I=[0, 1] and any m, n≥1, let N(n, f)denote the number of n-periodic orbits in f. Put N(n, m)=min{N(n, f):f is a continuousfunction on I, and N(m, f)≥1}. The famous Sarkovskii’s theorem can be stated as follows:If n?m, then N(n,m)≥1. In this paper, we further obtain analytic expressions of the precisevalue of N(n, m) for all positive integers m and n, which are convenient for computing. 展开更多
关键词 continuous function PERIODIC ORBIT sarkovskii’s theorem UNIMODAL orbit.
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一类中立型泛函微分方程周期解问题 被引量:7
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作者 鲁世平 葛渭高 郑祖庥 《数学年刊(A辑)》 CSCD 北大核心 2004年第5期645-652,共8页
本文利用Fourier级数理论和Mawhin重合度拓展定理研究一类中立型泛函微分方程的周期解存在性问题.在其对应的特征方程具有零特征根的条件下,得到了周期解存在性的新结果.
关键词 中立型泛函微分方程 周期解 FOURIER级数 特征根 特征方程 定理 存在性 问题 拓展 条件
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一类二阶时滞泛函微分方程周期解的存在与唯一性(英文) 被引量:3
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作者 汪娜 鲁世平 +1 位作者 章家顺 沈佐民 《安徽师范大学学报(自然科学版)》 CAS 2008年第5期409-414,共6页
我们利用Mawhin重合度拓展定理,研究了一类二阶时滞泛函微分方程x″(t)+f(t,x(t),x(t-τ))=p(t)周期解的存在唯一性问题,得到了其周期解存在唯一的新的结果.
关键词 周期解 时滞 泛函微分方程 mawhin拓展定理
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一类具偏变元高阶p-Laplace微分方程的周期解 被引量:11
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作者 张志戎 鲁世平 《吉林大学学报(理学版)》 CAS CSCD 北大核心 2011年第1期71-75,共5页
研究一类2n阶p-Laplace微分方程[φp(u(n)(t))](n)+f(u(n)(t))+g(t,u(t),u(t-τ(t)))=e(t),运用Mawhin重合度拓展定理,得到了其周期解的存在性.
关键词 周期解 mawhin拓展定理 具偏变元 P-LAPLACE方程
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