DARBOUX POLYNOMIALS AND NON-ALGEBRAIC INTEGRABILITY OF THE L SYSTEM

In this paper, we characterize all of the Darboux polynomials of the L system and prove that the system is not algebraically integrable, using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations.     

Poisson Stable Solutions for Stochastic Differential Equations with Lévy Noise

In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.     

Stochastic Nonlinear Beam Equations with Lévy Jump

In this paper,we study stochastic nonlinear beam equations with Lévy jump,and use Lyapunov functions to prove existence of global mild solutions and asymptotic stability of the zero solution.     

Exact Solutions of Fisher and Generalized Fisher Equations with Variable Coefficients

In this work,we consider a Fisher and generalized Fisher equations with variable coefficients.Usingtruncated Painlevé expansions of these equations,we obtain exact solutions of these equations with a constrainton the coefficients a(t)and b(t).     

一类系数为间隙级数的高阶线性微分方程解的增长性

In this paper, we investigate the growth of solutions of a class of higher order linear differential equations with coefficients being gap series. In this case, we remove the condition that the order of coefficients in equations is less than 1/2, and obtain some results which improve the previous results.     

Asymptotic and Oscillatory Behavior of Solutions of First Order Neutral Differential Equations

This paper has made researches on first order neutral differential equations with variable coefficients and several deviations. The asymptotic behavior of nonoscillatory solutions of the equations are discussed. Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained. The relevent results in [1—3] are improved and generalized .     

THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION WITH L~p INITIAL VALUE

The aim of this paper is to prove the well-posedness(existence and uniqueness) of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.     

THE LOCAL SOLVABILITY OF A CLASS OF PSEUDO-DIFFERENTIAL EQUATIONS OF PRINCIPAL TYPE

In 1970, Nirenberg and Treves gave the necessary and sufficient condition of the local solvability for linear partial differential equations of principal type with analytic coeffcients. Soon after, Beals and Fefferman studied the equations having only smooth coefficients.     

ON THE GROWTH AND VALUE DISTRIBUTION OF ANALYTIC SOLUTIONS OF A CLASS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

In this paper, we show that the growth of meromorphic or algebroidal solutions of some algebraic differential equations can be estimated in terms of the growth of the coefficients in tho equation and the counting functions of some value peints. We point simulteneously out that the growth of algebroid solutions of certain class of differential equations can be estimated using only the growth of coefficients in the equation, and give an example which is not belonging to this class to show that the above conclusion is not true.     

Modified Boussinesq System with Variable Coefficients： Classical Lie Approach and Exact Solutions

The Lie-group formalism is applied to investigate the symmetries of the modified Boussinesq system with variable coefficients. We derived the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The reduced systems of ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.     

SUBNORMAL SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

In this article, we apply the concept of hyper-order to higher order linear differential equations with periodic coefficients, investigate the existence and the form of its subnormal solution, and estimate the growth of all other solutions, and answer the question raised by Gundersen and Steinbart for more general periodic differential equations.     

Multivalued Stochastic Differential Equations with Non-Lipschitz Coefficients

The existence and uniqueness of solutions to the multivalued stochastic differential equations with non-Lipschitz coefficients are proved, and bicontinuous modifications of the solutions are obtained.     

Maximum principle for anticipated recursive stochastic optimal control problem with delay and Lvy processes

In this paper,we study the stochastic maximum principle for optimal control problem of anticipated forward-backward system with delay and Lvy processes as the random disturbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L′evy processes(AFBSDEDLs),we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs' preliminary result with certain classical convex variational techniques,the corresponding maximum principle is proved.     

On singular Lüroth quartics

Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called Lüroth quartics.The locus of singular Lüroth quartics has two irreducible components,both of codimension two in P14.We compute the degree of them and discuss the consequences of this computation on the explicit form of the Lüroth invariant.One important tool is the Cremona hexahedral equations of the cubic surface.We also compute the class in M 3 of the closure of the locus of nonsingular Lüroth quartics.     

Stability of weak solutions for the compressible Navier-Stokes-Poisson equations

In this paper, we consider the isentropic compressible Navier-Stokes-Poisson equations arising from transport of charged particles or motion of gaseous stars in astrophysics. We are interested in the case that the viscosity coefficients depend on the density and shall degenerate in the appearance of (density) vacuum, and show the L 1 -stability of weak solutions for arbitrarily large data on spatial multi-dimensional bounded or periodic domain or whole space.     

ASYMPTOTIC BEHAVIOR FOR NONOSCILLATORY SOLUTIONS OF REACTION-DIFFUSION DIFFERENTIAL EQUATIONS WITH SEVERAL DELAYS IN THE NEUTRAL TERM

In this paper, we first consider differential equations with several delays inthe neutral term of the formstudy various cases of coefficients in the neutral term and obtain the asymptoticbehavior for nonoscillatory solution of (1~*) under some hypotheses. Moreover,we consider reaction-diffusion differential equations with several delays in theneutral term of the formfor (t, x)∈ R~+ ×Ω. We also study various cases of coefficients in the neutralterm and obtain the asymptotic behavior for nonoscillatory solution of (2~*)under some hypotheses.     

二阶非线性中立型微分方程的振动性

This paper discusses a class of second order nonlinear neutral differential equations with variable coefficients and variable d eviations.Oscillation oriteria for all solutions of the equations are established and sufficient conditions are also given to ensure those derivatives of all differentiable solutions of the equatiors to be oscillatory.     

Stability for the Timoshenko Beam System with Local Kelvin-Voigt Damping

In this paper, we consider a vibrating beam with one segment made of viscoelastic material of a Kelvin-Voigt （shorted as K-V） type and other parts made of elastic material by means of the Timoshenko model. We have deduced mathematical equations modelling its vibration and studied the stability of the semigroup associated with the equation system. We obtain the exponential stability under certain hypotheses of the smoothness and structural condition of the coefficients of the system, and obtain the strong asymptotic stability under weaker hypotheses of the coefficients.     

Large deviation principle of stochastic differential equations with non-Lipschitzian coefficients

We study the large deviation principle of stochastic differential equations with non-Lipschitzian and non-homogeneous coefficients. We consider at first the large deviation principle when the coefficients σ and b are bounded, then we generalize the conclusion to unbounded case by using bounded approximation program. Our results are generalization of S. Fang-T. Zhang＇s results.     

Expression of meromorphic solutions of systems of algebraic differential equations with exponential coefficients

Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results.