The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-ma...The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-mathematics models, some conjectures and open problems appearing in literature are solved, and many known results are improved.展开更多
In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under d...In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained.展开更多
Examines the development of the composite legendre approximation in unbounded domains. Proof of the stability and convergence of a proposed scheme; Discussion of two-dimensional exterior problems; Error estimations.
In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results f...In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.展开更多
In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（...In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（RN ）. Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a（x） and k（x）.展开更多
This paper investigates the consensus problem of single integrator multi-agent systems with unbounded time-varying transmission delays and fixed di rec ted topology. A dist ributed cont roller is proposed taking into ...This paper investigates the consensus problem of single integrator multi-agent systems with unbounded time-varying transmission delays and fixed di rec ted topology. A dist ributed cont roller is proposed taking into consideration the unbounded transmission delays. It is shown that the consensus problem can be solved via the proposed controller under the spanning tree assumption and the nocycle assumption. The authors characterize the no-cycle assumption and prove the consensus of the concerned multi-agent systern with an induction procedure. Two simulation examples are provided, one to illustrate the effectiveness of our result and the other to show the necessity of the no-cycle assumption.展开更多
In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete oper...In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains.展开更多
In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, ...In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.展开更多
By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for...By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper.展开更多
This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic g...This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z.The existence and uniqueness results are given to these BSDEs.As an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.展开更多
基金Project partially supported by the National Nature Science Foundation of Chinathe Natural Scienee Foundation of Hunan Province.
文摘The global attractivity of the zero solution of the delay functional differential equation x(t)+ [1+x(t)]F(t, x(·)) =0 is studied by using a new technique. When this result is applied to some special delay bio-mathematics models, some conjectures and open problems appearing in literature are solved, and many known results are improved.
基金Supported by the NNSF of China(60464001) Guangxi Science Foundation(0575092).
文摘In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained.
文摘Examines the development of the composite legendre approximation in unbounded domains. Proof of the stability and convergence of a proposed scheme; Discussion of two-dimensional exterior problems; Error estimations.
基金The NNSF (10071031) of China China Postdoctoral Science Foundation.
文摘In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.
基金supported by National Natural Science Foundation of China (Grant Nos.10631030, 10871075)the PhD Specialized Grant of the Ministry of Education of China (Grant No. 20060511001)the Natural Science Foundation of Guangdong Province, China (Grant No. 9451064201003736)
文摘In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 【 q 【 2 , 0≤μ 【 μˉ=（N-2）2<sub>4</sub> , a（x）, k（x） ∈ C（RN ）. Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a（x） and k（x）.
基金supported by the Research Grants Council of Hong Kong under Grant No.CityU-11206817
文摘This paper investigates the consensus problem of single integrator multi-agent systems with unbounded time-varying transmission delays and fixed di rec ted topology. A dist ributed cont roller is proposed taking into consideration the unbounded transmission delays. It is shown that the consensus problem can be solved via the proposed controller under the spanning tree assumption and the nocycle assumption. The authors characterize the no-cycle assumption and prove the consensus of the concerned multi-agent systern with an induction procedure. Two simulation examples are provided, one to illustrate the effectiveness of our result and the other to show the necessity of the no-cycle assumption.
文摘In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains.
基金NSFC!( 1 9671 0 1 7) and NSF!( A970 1 2 ) of Fujian.
文摘In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.
基金Supported by the National Natural Science Foundation of China(No.10671167)the Natural Science Foundation of Liaocheng University(31805)
文摘By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper.
基金supported by the National Natural Science Foundation of China(Nos.11631004,12031009).
文摘This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z.The existence and uniqueness results are given to these BSDEs.As an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.
