This paper is concerned with nonplanar traveling fronts for delayed reaction- diffusion equation with bistable nonlinearity in RTM （m〉 3）. By the comparison principle and super- and subsolutions technique, we estab...This paper is concerned with nonplanar traveling fronts for delayed reaction- diffusion equation with bistable nonlinearity in RTM （m〉 3）. By the comparison principle and super- and subsolutions technique, we establish the existence of pyra- midal traveling fronts.展开更多
In this paper we consider eigenvalue asymptotic estimations for a class of structured matrices arising from statistical applications. The asymptotic upper bounds of the largest eigenvalue(λmax) and the sum of squares...In this paper we consider eigenvalue asymptotic estimations for a class of structured matrices arising from statistical applications. The asymptotic upper bounds of the largest eigenvalue(λmax) and the sum of squares of eigenvalues(■)are derived. Both these bounds are useful in examining the stability of certain Markov process. Numerical examples are provided to illustrate tightness of the bounds.展开更多
An autonomous stage-structured competitive systems with toxic effect is investigated in this paper. Sufficient conditions which guarantee the global attractivity of the system and the extinction of the partial species...An autonomous stage-structured competitive systems with toxic effect is investigated in this paper. Sufficient conditions which guarantee the global attractivity of the system and the extinction of the partial species are obtained, respectively. Our results supplement and compliment one of the main results of Liu and Li [Global stability analysis of a nonautonomous stage-structured competitive system with toxic effect and double maturation delays, Abstract and Applied Analysis, Volume 2014, Article ID 689573, 15 pages].展开更多
In this paper, we introduce the application of random matrices in mathe- matical physics including Riemann-Hilbert problem, nuclear physics, big data, image processing, compressed sensing and so on. We start with the ...In this paper, we introduce the application of random matrices in mathe- matical physics including Riemann-Hilbert problem, nuclear physics, big data, image processing, compressed sensing and so on. We start with the Riemann- Hilbert problem and state the relation between the probability distribution of nontrivial zeros and the eigenvalues of the random matrices. Through the random matrices theory, we derive the distribution of Neutron width and prob- ability density between energy levels. In addition, the application of random matrices in quantum chromo dynamics and two dimensional Einstein gravity equations is also present in this paper.展开更多
This paper deals with the oscillatory properties of a class of nonlinear advanced difference equations. Sufficient criteria in the form of infinite sum for the equation to be oscillatory are obtained. In the linear ca...This paper deals with the oscillatory properties of a class of nonlinear advanced difference equations. Sufficient criteria in the form of infinite sum for the equation to be oscillatory are obtained. In the linear cases, our results coincide with those in the literature.展开更多
In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In o...In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.展开更多
This paper deals with the blow-up properties of positive solutions to a degenerate and singular nonlocal parabolic equation with weighted nonlocal boundary conditions. Under appropriate hypotheses, the global existenc...This paper deals with the blow-up properties of positive solutions to a degenerate and singular nonlocal parabolic equation with weighted nonlocal boundary conditions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, by using the properties of Green＇s function, we find that the blow-up set of the blow-up solution is the whole domain （0, a）, and this differs from parabolic equations with local sources case.展开更多
The main purpose of this paper is to explore the existence of positive periodic solutions to impulsive predator-prey systems with type IV functional responses. Sufficient criteria are obtained for the existence of str...The main purpose of this paper is to explore the existence of positive periodic solutions to impulsive predator-prey systems with type IV functional responses. Sufficient criteria are obtained for the existence of strictly positive periodic solutions. The approach is based on a continuation theorem in the coincidence degree theory as well as some prior estimates. This is also the first time that multiple positive periodic solutions are obtained using coincidence degree theory in impulsive ecological systems.展开更多
This paper is concerned with traveling wave solutions to a nonlocal dispersal epide- mic model. Combining the upper and lower solutions and monotone iteration method, we establish the existence of nondecreasing travel...This paper is concerned with traveling wave solutions to a nonlocal dispersal epide- mic model. Combining the upper and lower solutions and monotone iteration method, we establish the existence of nondecreasing traveling wave fronts for the speed being larger than the critical one. Furthermore, by the approximation method, the existence of traveling wave fronts for the critical speed is established as well. Finally, we discuss the nonexistence of traveling wave fronts for the speed being smaller than critical one by Laplace transform.展开更多
基金supported by NNSF of China(11071105,11371179)the Program for New Century Excellent Talents in University(NCET-10-0470)
文摘This paper is concerned with nonplanar traveling fronts for delayed reaction- diffusion equation with bistable nonlinearity in RTM （m〉 3）. By the comparison principle and super- and subsolutions technique, we establish the existence of pyra- midal traveling fronts.
基金Juan Liang’s work was supported by Young and middle-aged teachers education research project of Fujian Provincial Education Department No.JT180300Jiangzhou Lai’s work was supported by Core Courses for undergraduate majors of Fuzhou university No.0360-52000732Qiang Niu’s work was supported by XJTLU research enhancement fund No.REF-18-01-04 and the XJTLU Key Programme Special Fund(KSF)
文摘In this paper we consider eigenvalue asymptotic estimations for a class of structured matrices arising from statistical applications. The asymptotic upper bounds of the largest eigenvalue(λmax) and the sum of squares of eigenvalues(■)are derived. Both these bounds are useful in examining the stability of certain Markov process. Numerical examples are provided to illustrate tightness of the bounds.
基金supported by the Natural Science Foundation of Fujian Province(2015J01012,2015J01019)
文摘An autonomous stage-structured competitive systems with toxic effect is investigated in this paper. Sufficient conditions which guarantee the global attractivity of the system and the extinction of the partial species are obtained, respectively. Our results supplement and compliment one of the main results of Liu and Li [Global stability analysis of a nonautonomous stage-structured competitive system with toxic effect and double maturation delays, Abstract and Applied Analysis, Volume 2014, Article ID 689573, 15 pages].
文摘In this paper, we introduce the application of random matrices in mathe- matical physics including Riemann-Hilbert problem, nuclear physics, big data, image processing, compressed sensing and so on. We start with the Riemann- Hilbert problem and state the relation between the probability distribution of nontrivial zeros and the eigenvalues of the random matrices. Through the random matrices theory, we derive the distribution of Neutron width and prob- ability density between energy levels. In addition, the application of random matrices in quantum chromo dynamics and two dimensional Einstein gravity equations is also present in this paper.
基金This work is supported by National Natural Science Foundation of China (No.40373003, 40372121) CUGQNL0517.
文摘This paper deals with the oscillatory properties of a class of nonlinear advanced difference equations. Sufficient criteria in the form of infinite sum for the equation to be oscillatory are obtained. In the linear cases, our results coincide with those in the literature.
基金Supported by NNSF of China(11201213,11371183)NSF of Shandong Province(ZR2010AM022,ZR2013AM004)+2 种基金the Project of Shandong Provincial Higher Educational Science and Technology(J15LI07)the Project of Ludong University High-Quality Curriculum(20130345)the Teaching Reform Project of Ludong University in 2014(20140405)
文摘In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.
基金supported partially by the foundation of professors and doctors of Yancheng Normal University(14YSYJB0106)by the research scheme of the natural science of the universities of Jiangsu Province(08KJD110017 and 13KJB110028)
文摘This paper deals with the blow-up properties of positive solutions to a degenerate and singular nonlocal parabolic equation with weighted nonlocal boundary conditions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, by using the properties of Green＇s function, we find that the blow-up set of the blow-up solution is the whole domain （0, a）, and this differs from parabolic equations with local sources case.
基金National Natural Science Foundation of China(#10671069).
文摘The main purpose of this paper is to explore the existence of positive periodic solutions to impulsive predator-prey systems with type IV functional responses. Sufficient criteria are obtained for the existence of strictly positive periodic solutions. The approach is based on a continuation theorem in the coincidence degree theory as well as some prior estimates. This is also the first time that multiple positive periodic solutions are obtained using coincidence degree theory in impulsive ecological systems.
文摘This paper is concerned with traveling wave solutions to a nonlocal dispersal epide- mic model. Combining the upper and lower solutions and monotone iteration method, we establish the existence of nondecreasing traveling wave fronts for the speed being larger than the critical one. Furthermore, by the approximation method, the existence of traveling wave fronts for the critical speed is established as well. Finally, we discuss the nonexistence of traveling wave fronts for the speed being smaller than critical one by Laplace transform.
