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The Existence and Uniqueness of Periodic Solutions for a Kind of Lienard Equation with a Deviating Argument 被引量:2
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作者 WANG Na 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期74-80,共7页
By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of pe... By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained. 展开更多
关键词 periodic solution deviating argument lie’nard equations continuation theorem
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The Existence of Periodic Solutions of a Class of <i>n</i>-Degree Polynomial Differential Equations*
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作者 Ni Hua 《Applied Mathematics》 2021年第1期32-57,共26页
This paper deals with a class of <em>n</em>-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (<em>n</em> is an odd... This paper deals with a class of <em>n</em>-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (<em>n</em> is an odd number) or two (<em>n</em> is an even number) periodic solutions of the equation is obtained. These conclusions have certain application value for judging the existence of periodic solutions of polynomial differential equations with only one higher-order term. 展开更多
关键词 n-degree Polynomial Differential equation Fixed Point Theory periodic solution
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TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN 被引量:5
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作者 金春花 杨彤 《Acta Mathematica Scientia》 SCIE CSCD 2016年第4期1015-1029,共15页
This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of th... This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given. 展开更多
关键词 Time periodic solution compressible Navier-Stokes equation topology degree energy method
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Existence of Periodic Solutions for Generalized Liénard-Typed Functional Differential Equations
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作者 贺小明 葛渭高 单文锐 《Journal of Beijing Institute of Technology》 EI CAS 2002年第3期325-328,共4页
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ... The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended. 展开更多
关键词 functional differential equation periodic solution coincidence degree
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Existence and uniqueness of periodic solutions for forced Liénard-type equations
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作者 LIU Bing-wen 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第3期295-302,共8页
By using topological degree theory and some analysis skill, some sufficient conditions for the existence and uniqueness of periodic solutions for a class of forced Lienard-type equations are obtained.
关键词 periodic solution lienard equation topological degree
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Nonrecurrence Theorems of Periodic Solutions for Functional Differential Equations
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作者 翟延慧 黄庆道 韩月才 《Northeastern Mathematical Journal》 CSCD 2002年第2期137-144,共8页
nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.
关键词 Nonrecurrence of boundary periodic solution functional differential equation topological degree.
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Existence of periodic solutions for Lienard equations with finite delay
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作者 Wei, JJ Huang, QC 《Chinese Science Bulletin》 SCIE EI CAS 1997年第14期1145-1149,共5页
THE existence of periodic solutions of Lienard equation with finite delay x(t) + f(x(t))x(t) + g(x(t-r))=0 (1)has been studied extensively. However, most works we have so far require the assumption thatx·g(x)】0 ... THE existence of periodic solutions of Lienard equation with finite delay x(t) + f(x(t))x(t) + g(x(t-r))=0 (1)has been studied extensively. However, most works we have so far require the assumption thatx·g(x)】0 for all x∈R, x≠0, which is not true for some equations with strong practicalbackground. For example, the sunflower 展开更多
关键词 DELAY lienard equationS BIFURCATIONS periodic solutions.
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Periodic Solutions of Lienard Equations withInfinite Delay
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作者 彭世国 朱思铭 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2003年第1期98-102,共5页
The problem of periodic solutions for Lienard equations with infinite delay x+(?)x+g(t,xt)=p(t)is discussed by using Mawhin's,coincidence degree theory. Some new results on the existence of periodic solutions are ... The problem of periodic solutions for Lienard equations with infinite delay x+(?)x+g(t,xt)=p(t)is discussed by using Mawhin's,coincidence degree theory. Some new results on the existence of periodic solutions are derived. 展开更多
关键词 lienard equations infinite delay periodic solutions.
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ON THE NONEXISTENCE OF PERIODIC SOLUTIONS FOR LIENARD-TYPE EQUATIONS 被引量:1
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作者 ZHOU Jin(Department of Applied Mathematics, Hebei University of Technology, Tianjin 300130, China) 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1999年第2期184-192,共9页
In this paper, we investigate the nonexistence of periodic solutions for Lienardtype equationSome brief and practical sufficient conditions on the nonexistence of periodic solutions aregiven. Our results can be easily... In this paper, we investigate the nonexistence of periodic solutions for Lienardtype equationSome brief and practical sufficient conditions on the nonexistence of periodic solutions aregiven. Our results can be easily applied to the well-known Lienard equation x+f(x) x +g(x) =0, and substantially extend and improve some known results. 展开更多
关键词 lienard-type equationS lienard system periodic solutions nonexistence.
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On the Existence of Positive Periodic Solutions for Neutral Functional Differential Equation with Multiple Deviating Arguments 被引量:37
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作者 Shi-pingLu Wei-gaoGe 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2003年第4期631-640,共10页
By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following n... By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutions of following neutral functional differential equation 展开更多
关键词 Positive periodic solution k-set contraction coincidence degree neutral functional differential equation
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EXISTENCE OF PERIODIC SOLUTION FOR A KIND OF THIRD-ORDER GENERALIZED NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH VARIABLE PARAMETER
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作者 A.M.Mahmoud E.S.Farghaly 《Annals of Applied Mathematics》 2018年第3期285-301,共17页
In this paper, we investigate a third-order generalized neutral functional differential equation with variable parameter. Based on Mawhin’s coincidence degree theory and some analysis skills, we obtain sufficient con... In this paper, we investigate a third-order generalized neutral functional differential equation with variable parameter. Based on Mawhin’s coincidence degree theory and some analysis skills, we obtain sufficient conditions for the existence of periodic solution for the equation. An example is also provided. 展开更多
关键词 existence of periodic solution third-order neutral functional differential equation variable parameter Mawhin's continuation theorem coincidence degree
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Existence and Uniqueness of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equations with Constant Delays 被引量:5
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作者 Bing-wen Liu Li-hong Huang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2006年第2期287-296,共10页
In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays o... In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form (x(t)+Bx(t-δ))"+Cx'(t)+g(x(t-τ))=p(t). 展开更多
关键词 Second Order neutral functional differential equations constant delay periodic solutions coincidence degree
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2π-periodic Solution for a Kind High Order Delay Duffing Equation 被引量:4
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作者 LIN Wen-xian 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第1期85-89,共5页
In this paper, the high order delay Duffing equation ax^(2n) +bx+g(x(t-r)) = p(t) are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic s... In this paper, the high order delay Duffing equation ax^(2n) +bx+g(x(t-r)) = p(t) are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic solution is obtained. 展开更多
关键词 Duffing equation periodic solution coincidence degree
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Existence of Periodic Solutions for Neutral Functional Differential Equations with Nonlinear Difference Operator 被引量:1
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作者 Shi Ping LU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第12期1541-1556,共16页
In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible ... In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field. 展开更多
关键词 Neutral functional differential equation condensing operator topological degree periodic solution
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PERIODIC SOLUTIONS OF THIRD-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS 被引量:2
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作者 Zhang Zhengqiu Wang ZhichengDept.ofAppl.Math.,HunanUniv.,Changsha410082,China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第2期145-154,共10页
The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1... The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions 展开更多
关键词 periodic solution abstract continuation theorem a- priori estimate coincidence degree functional differential equation
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EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF HIGHER ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH TWO DEVIATING ARGUMENTS 被引量:2
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作者 Li Xiaojing (College of Math. and Phy., Jiangsu Teachers University of Tech., Changzhou 213015, Jiangsu) Zhang Zhirong, Lu Shiping (Dept. of Math., Anhui Normal University, Wuhu 241000, Anhui) 《Annals of Differential Equations》 2008年第3期289-298,共10页
In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating argum... In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained. 展开更多
关键词 periodic solution higher order functional differential equation coin-cidence degree theory
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A RESULT ON PERIODIC SOLUTIONS OF SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS
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作者 张正球 《Annals of Differential Equations》 2004年第2期208-214,共7页
We obtain sufficient condition for the existence of periodic solutions of thefollowing second order functional differential equationsx'(t) + ax'~α(t) + bf(x(t)) + g(x(t-T_1), x'(t-T_2))=p(t)=p(t+2π).Our ... We obtain sufficient condition for the existence of periodic solutions of thefollowing second order functional differential equationsx'(t) + ax'~α(t) + bf(x(t)) + g(x(t-T_1), x'(t-T_2))=p(t)=p(t+2π).Our approach is based on the continuation theorem of coincidence degree, andthe α-priori: estimate of periodic solutions. 展开更多
关键词 periodic solutions the continuation theorem coincidence degree functional differential equations the property of Brouwer degree
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EXISTENCE OF PERIODIC SOLUTIONS TO A LINARD EQUATION WITH MULTIPLE DELAYS
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作者 Ming Jia(College of International Exchange,Central South University of Forestry and Technology,Changsha 410004) Jianhua Shen(College of Science,Hangzhou Normal University,Hangzhou 310036) 《Annals of Differential Equations》 2011年第3期331-335,共5页
In this paper,by a coincidence degree theory,the existence of periodic solutions to a Linard equation with multiple delays is established,which substantially extends some results in the previous literatures.
关键词 coincidence degree theory periodic solutions Linard equation mul-tiple delays
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EXISTENCE OF PERIODIC SOLUTION TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT
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作者 Lijun Pan (Dept. of Math.,Jiaying University,Meizhou 514015,Guangdong) 《Annals of Differential Equations》 2009年第3期323-331,共9页
In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of perio... In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results. 展开更多
关键词 higher order functional differential equations deviating argument periodic solution coincidence degree
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EXISTENCE OF PERIODIC SOLUTIONS TO THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATION
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作者 A.M.A.Abou-El-Ela A.I.Sadek R.O.A.Taie 《Annals of Differential Equations》 2011年第4期409-417,共9页
By means of the continuation theorem of the coincidence degree theory and analysis techniques,sufficient conditions for the existence of periodic solutions to a kind of third-order neutral delay functional differentia... By means of the continuation theorem of the coincidence degree theory and analysis techniques,sufficient conditions for the existence of periodic solutions to a kind of third-order neutral delay functional differential equation with deviating arguments are obtained. 展开更多
关键词 periodic solutions coincidence degree deviating arguments thirdorder non-autonomous delay differential equations
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