This paper is mainly concerned with the S-asymptotically Bloch type periodicity.Firstly,we introduce a new notion of S-asymptotically Bloch type periodic functions,which can be seen as a generalization of concepts of ...This paper is mainly concerned with the S-asymptotically Bloch type periodicity.Firstly,we introduce a new notion of S-asymptotically Bloch type periodic functions,which can be seen as a generalization of concepts of S-asymptoticallyω-periodic functions and S-asymptoticallyω-anti-periodic functions.Secondly,we establish some fundamental properties on S-asymptotically Bloch type periodic functions.Finally,we apply the results obtained to investigate the existence and uniqueness of S-asymptotically Bloch type periodic mild solutions to some semi-linear differential equations in Banach spaces.展开更多
In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by me...In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.展开更多
In this paper we analyze the qualitative behaviour of the equation ε+q(X) +εX=bp(t), where e is a small parameter.We divide the interval of parameter b into four sets of subintervals,A, B,C and D.For bA,B or D,we di...In this paper we analyze the qualitative behaviour of the equation ε+q(X) +εX=bp(t), where e is a small parameter.We divide the interval of parameter b into four sets of subintervals,A, B,C and D.For bA,B or D,we discuss the different structures of the attractors of the equation and their stabilities.When chaotic phenomena appear,we also estimate the entropy.For bC,the set of bifurcation intervals,we analyze the bifurcating type and get a series of consequences from the results of Newhouse and Palis.展开更多
In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence o...In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.展开更多
In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic...In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic lattice cell is not necessarily rectangular. After appropriately foring the gange, the model can be formulated as a system of nonlinear parabolic partial differential equations with quasi-periodic boundary conditions. We first give some results concerning the existence, uniqueness and regularity of solutions and then we propose a semiimplicit finite element scheme solving the system of nonlinear partial dmerential equations and show the optimal error estimates both in the L2 and energy norm.We also report on some numerical results at the end of the paper.展开更多
In this paper a mathematical model of chemical systems is investigated.We present the conditions for the existence and local stability of the steady statesand the periodic solution of the Hopf type.Specifically,we sho...In this paper a mathematical model of chemical systems is investigated.We present the conditions for the existence and local stability of the steady statesand the periodic solution of the Hopf type.Specifically,we show by using an ana-lytical method that there may exist two or four Hopf bifurcation points separatedat a finite distance from each other;at the same time,a technique for studying theHopf bifurcation value is given.展开更多
In this paper, a mathematical model of competition between plasmid-bearing and plasmidfree organisms in a chemostat with an inhibitor is investigated. The model is in the form of a system of nonlinear differential eq...In this paper, a mathematical model of competition between plasmid-bearing and plasmidfree organisms in a chemostat with an inhibitor is investigated. The model is in the form of a system of nonlinear differential equations. By using qualitative methods, the conditions for the existence and local stability of the equilibria are obtained. The existence and stability of periodic solutions of the Hopf type are studied. Numerical simulations about the Hop f bifurcation value and Hopf limit cycle are also given.展开更多
基金supported by NSF of Shaanxi Province(2020JM-183).
文摘This paper is mainly concerned with the S-asymptotically Bloch type periodicity.Firstly,we introduce a new notion of S-asymptotically Bloch type periodic functions,which can be seen as a generalization of concepts of S-asymptoticallyω-periodic functions and S-asymptoticallyω-anti-periodic functions.Secondly,we establish some fundamental properties on S-asymptotically Bloch type periodic functions.Finally,we apply the results obtained to investigate the existence and uniqueness of S-asymptotically Bloch type periodic mild solutions to some semi-linear differential equations in Banach spaces.
文摘In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.
文摘In this paper we analyze the qualitative behaviour of the equation ε+q(X) +εX=bp(t), where e is a small parameter.We divide the interval of parameter b into four sets of subintervals,A, B,C and D.For bA,B or D,we discuss the different structures of the attractors of the equation and their stabilities.When chaotic phenomena appear,we also estimate the entropy.For bC,the set of bifurcation intervals,we analyze the bifurcating type and get a series of consequences from the results of Newhouse and Palis.
文摘In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.
文摘In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic lattice cell is not necessarily rectangular. After appropriately foring the gange, the model can be formulated as a system of nonlinear parabolic partial differential equations with quasi-periodic boundary conditions. We first give some results concerning the existence, uniqueness and regularity of solutions and then we propose a semiimplicit finite element scheme solving the system of nonlinear partial dmerential equations and show the optimal error estimates both in the L2 and energy norm.We also report on some numerical results at the end of the paper.
基金Supported by the Chinese National Science Foundation"Tian Yuan"Terms and LNM Institute of Mechanics,Chinese Academy of Sciences
文摘In this paper a mathematical model of chemical systems is investigated.We present the conditions for the existence and local stability of the steady statesand the periodic solution of the Hopf type.Specifically,we show by using an ana-lytical method that there may exist two or four Hopf bifurcation points separatedat a finite distance from each other;at the same time,a technique for studying theHopf bifurcation value is given.
文摘In this paper, a mathematical model of competition between plasmid-bearing and plasmidfree organisms in a chemostat with an inhibitor is investigated. The model is in the form of a system of nonlinear differential equations. By using qualitative methods, the conditions for the existence and local stability of the equilibria are obtained. The existence and stability of periodic solutions of the Hopf type are studied. Numerical simulations about the Hop f bifurcation value and Hopf limit cycle are also given.
