The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As a...The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions.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 periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extr...The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.展开更多
Existence and nonexistence criteria are established for the positive periodic solutions of two species population growth with periodic delay by applying continuation theorem of coincidence degree theory.
In this paper,we study the existence of"weak solution"for a class of p(x)-Kirchhoff type problem involving the p(x)-Laplacian-like operator depending on two real parameters with Neumann boundary condition.Us...In this paper,we study the existence of"weak solution"for a class of p(x)-Kirchhoff type problem involving the p(x)-Laplacian-like operator depending on two real parameters with Neumann boundary condition.Using a topological degree for a class of demicontinuous operator of generalized(S_(+))type and the theory of the variable exponent Sobolev space,we establish the existence of"weak solution"of this problem.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
In this paper,a class of discrete time non-autonomous competing system with feedback controls is considered. With the help of differential equations with piecewise constant arguments,we first propose a discrete model ...In this paper,a class of discrete time non-autonomous competing system with feedback controls is considered. With the help of differential equations with piecewise constant arguments,we first propose a discrete model of a continuous non-autonomous competing system with feedback controls. Then,using the coincidence degree and the related continuation theorem as well as some priori estimations,a suficient condition for the existence of positive solutions to difference equations is obtained.展开更多
In this paper, by using the topological degree method and some limiting arguments, the existence of admissible periodic bouncing solutions for a class of non-conservative semi-linear impact equations is proved.
By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete...By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.展开更多
This paper gives upper and lower solutions methods for the existence of solutions of periodic BVP for second order Duffing equation x" + kx’+ g(t, x) = 0, x(0) = x(T), x’(0) = x’(T),where g is a Caratheodory f...This paper gives upper and lower solutions methods for the existence of solutions of periodic BVP for second order Duffing equation x" + kx’+ g(t, x) = 0, x(0) = x(T), x’(0) = x’(T),where g is a Caratheodory function. As an application, some existence theorems are given for the equation x" + kx’ + g(t, x) = s, x(0) = x(T), x’(0) = x’(T),with respect to a real parameter s.展开更多
In this paper, the existence o f a positive periodic solution to the following neutral predator_prey system (t)=rH(t)1-a 1(t)H(t-τ)+a 2(t-τ)K-α(t)H(t)P(t), (t)=-b(t)P(t)+β(t)H(t)P(t) is studied,in which ...In this paper, the existence o f a positive periodic solution to the following neutral predator_prey system (t)=rH(t)1-a 1(t)H(t-τ)+a 2(t-τ)K-α(t)H(t)P(t), (t)=-b(t)P(t)+β(t)H(t)P(t) is studied,in which r,a 2,K and τ are positive constants, and a 1(t ),α(t),b(t) and β(t) are positive continuous functions of period ω .展开更多
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generaliz...In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.展开更多
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixe...E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.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
By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]...By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].展开更多
文摘The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions.
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 periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.
文摘Existence and nonexistence criteria are established for the positive periodic solutions of two species population growth with periodic delay by applying continuation theorem of coincidence degree theory.
文摘In this paper,we study the existence of"weak solution"for a class of p(x)-Kirchhoff type problem involving the p(x)-Laplacian-like operator depending on two real parameters with Neumann boundary condition.Using a topological degree for a class of demicontinuous operator of generalized(S_(+))type and the theory of the variable exponent Sobolev space,we establish the existence of"weak solution"of this problem.
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 National Natural Science Foundation of China (No.10771215)the Scientific Research Initializing Foundation of Hunan Institute of Engineering (0744)
文摘In this paper,a class of discrete time non-autonomous competing system with feedback controls is considered. With the help of differential equations with piecewise constant arguments,we first propose a discrete model of a continuous non-autonomous competing system with feedback controls. Then,using the coincidence degree and the related continuation theorem as well as some priori estimations,a suficient condition for the existence of positive solutions to difference equations is obtained.
基金Supported by the NNSF of China(11571249)NSF of JiangSu Province(BK20171275)Supported by the grant of Innovative Training Program of College Students in Jiangsu province(201410324001Z)
文摘In this paper, by using the topological degree method and some limiting arguments, the existence of admissible periodic bouncing solutions for a class of non-conservative semi-linear impact equations is proved.
基金Supported by the National Natural Science Foundation of China(No.10171044)the Natural Science Foundation of Jiangsu Province(No.BK2001024)the Foundation for University Key Teachers of the Ministry of Education of China
文摘By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.
文摘This paper gives upper and lower solutions methods for the existence of solutions of periodic BVP for second order Duffing equation x" + kx’+ g(t, x) = 0, x(0) = x(T), x’(0) = x’(T),where g is a Caratheodory function. As an application, some existence theorems are given for the equation x" + kx’ + g(t, x) = s, x(0) = x(T), x’(0) = x’(T),with respect to a real parameter s.
文摘In this paper, the existence o f a positive periodic solution to the following neutral predator_prey system (t)=rH(t)1-a 1(t)H(t-τ)+a 2(t-τ)K-α(t)H(t)P(t), (t)=-b(t)P(t)+β(t)H(t)P(t) is studied,in which r,a 2,K and τ are positive constants, and a 1(t ),α(t),b(t) and β(t) are positive continuous functions of period ω .
文摘In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
基金Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
文摘E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.
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By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].
