PERMANENCE AND PERIODIC SOLUTION FOR NONAUTONOMOUS COMPETITION-PREDATOR SYSTEM WITH TYPE II FUNCTIONAL RESPONSE

A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system is a periodic one, a set of easily verifiable suflficient conditions which guarantee the existence, uniqueness and global attractivity of a strictly positive periodic solution are ob-tained.     

Existence and global attractivity of unique positive almost periodic solution for a model of hematopoiesis

Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.     

Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.     

PERIODIC OSCILLATORY SOLUTION TO DELAYED BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS

In this paper,using the continuation theorem of coincidence degree theory,Lyapu- nov functionals and some new inequality techniques,some new sufficient criteria are obtained to ensure the existence and global exponential stability of periodic solution. Our results are less restrictive than previous works and more effective than those in [12],which plays a significant role in designing globally exponentially stable and peri- odic oscillatory BAM neural networks with periodic coefficients.One example is al...     

具有时滞的半比率依赖型捕食者-食饵系统的周期性

A delayed semi-ratio-dependent predator-prey system in a periodic environment is investigated in this paper. By using a continuation theorem based on Gaines and Mawhin‘s coincidence degree,the global existence of positive periodic solution is studied. A set of easily verifiable sufficient conditions are obtained.     

Persistence and Periodic Solution on a Nonautonomous SIS Model with Delays

An SIS model with periodic maximum infectious force,recruitment rate and removal rate of the infectives has been investigated in this articale.Sufficient conditions for the permanence and extinction of the disease are obtained.Furthermore,The existence and global stability of positive periodic solution are established.Finally,we present a procedure by which one can control the parameters of the model to kccp the infcctivcs stay eventually in a desired set.     

THE VACUUM IN NONISENTROPIC GAS DYNAMICS Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

We investigate the vacuum in nonisentropic gas dynamics in one space variable,with the most general equation of states allowed by thermodynamics.We recall physical constraints on the equations of state and give explicit and easily checkable conditions under which vacuums occur in the solution of the Riemann problem.We then present a class of models for which the Riemann problem admits unique global solutions without vacuums.     

The shape of limit cycles for a class of quintic polynomial differential systems

We consider the problem of finding limit cycles for a class of quintic polynomial differential systems and their global shape in the plane. An answer to this problem can be given using the averaging theory. More precisely, we analyze the global shape of the limit cycles which bifurcate from a Hopf bifurcation and periodic orbits of the linear center ẋ = −y, ẏ = x, respectively.     

EXISTENCE AND GLOBAL ATTRACTIVITY OF PERIODIC SOLUTIONS TO A PREDATOR-PREY SYSTEM WITH DELAYS AND IMPULSES

By using Gaines and Mawhin's continuation theorem of coincidence degree theory and constructing Lyapunov functionals,a set of easily verifiable sufficient conditions are derived for the existence and global attractivity of a positive periodic solution to a predator-prey system with delays and impulses.     

On Mixed Pressure-Velocity Regularity Criteria to the Navier-stokes Equations in Lorentz Spaces,Part Ⅱ:The Non-slip Boundary Value Problem

This paper is a continuation of the authors recent work [Beir?o da Veiga, H.and Yang, J., On mixed pressure-velocity regularity criteria to the Navier-Stokes equations in Lorentz spaces, Chin. Ann. Math., 42(1), 2021, 1–16], in which mixed pressure-velocity criteria in Lorentz spaces for Leray-Hopf weak solutions of the three-dimensional NavierStokes equations, in the whole space R~3 and in the periodic torus T~3, are established. The purpose of the present work is to extend the result of mentio...     

Two Characterizations of Diffeomorphisms of Euclidean Space

Two characterizations for a local diffeomorphism of R^n to be global one are given in terms of associated Wazewski equations.The two characterizations could be useful for the investigation of the Jacobian conjecture.     

Periodicity in a “Food-limited” Population Model with Toxicants and Time Delays

Abstract   With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, we study the global existence of positive periodic solutions of a “food-limited population model with toxicants and time delays. Some new results are obtained. Supported by the National Natural Sciences Foundation of China (No.10171010), the Key Project on Sciences and Technology of the Ministry of Education of China (No. Key 01061) and the Natural Sciences Foundation for Young Scholar of Northeast Normal University.     

Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems

This paper is devoted to the study ofthe existence of single and multiple positive solutions forthe first order boundary value problem x′= f(t,x),x(0)=x(T),where f ∈ C([0,T]×R).In addition,weapply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at theorigin.Our proofs are based on a fixed point theorem in cones.Our results improve some recent results in theliteratures.     

A new proof of <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the parabolic polyharmonic equations

In this paper we obtain local L ^p estimates for the parabolic polyharmonic equations by a straightforward approach. Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017)     

Complexity of Reducing the Delay between Two Nodes by Node-based and Edge-based Upgrading Strategies

For a pair of nodes s, t in an undirected graph G = (V, A) and a given level U of allowable delay, we would like to modify the network by node-based or edge-based upgrading strategies to make the delay between s and t not greater than U. In this paper, we present some NP-hard results for the delay improvement problems.     

<Emphasis Type="Italic">W</Emphasis><Superscript>1,<Emphasis Type="Italic">p</Emphasis></Superscript>(R<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>)-boundedness for maximal functions

In this paper, we get W ^1,p (R ⁿ )-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and Tananka’s results. Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural Science Foundation of China.     

A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems

In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming （SQP）, a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming （QP） which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.     

The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness

The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities.     

Exact traveling wave solutions and dynamical behavior for the (<Emphasis Type="Italic">n</Emphasis> + 1)-dimensional multiple sine-Gordon equation

Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. This work was supported by the National Natural Science Foundation of China (Grant No. 11671179) and the Natural Science Foundation of Yunnan Province (Grant No. 2005A0092M).     

Applications of an Explicit Formula for the Generalized Euler Numbers

The authors establish an explicit formula for the generalized Euler NumbersE2n^（x）, and obtain some identities and congruences involving the higher＇order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.