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
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
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
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
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.
nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
基金Foundation item: Supported by the Anhui Natural Science Foundation(050460103) Supported by the NSF of Anhui Educational Bureau(KJ2008B247) Supported by the RSPYT of Anhui Educational Bu- reau(2008jq1111)
文摘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.
文摘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.
基金supported by the Program for New Century Excellent Talents in University of the Ministry of Education(NCET-13-0804)NSFC(11471127)+3 种基金Guangdong Natural Science Funds for Distinguished Young Scholar(2015A030306029)The Excellent Young Teachers Program of Guangdong Province(HS2015007)Pearl River S&T Nova Program of Guangzhou(2013J2200064)supported by the General Research Fund of Hong Kong,City U 104511
文摘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.
文摘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.
基金Scientific Research Fund of Zhejiang Provincial Education Department (20070605)
文摘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.
文摘nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.
文摘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
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China (No.19871005).
文摘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
文摘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.
基金Supported by the National Natural Science Foundation of China(No.10371034)the Hunan Provincial Natural Science Foundation of China(05JJ40009).
文摘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).
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China(1 9971 0 2 6 )
文摘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
基金Natural Science Foundation of Anhui Province (050460103)the Key Natural Science Foundation by the Bureau of Education of Anhui Province(KJ2008A05ZC).
文摘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.
基金The project is supported by NNSF of China(No.10271044)
文摘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.
文摘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.
基金Supported by the Natural Science Foundation of Guangdong Province (No.9151063301000008)
文摘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.
文摘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.