LIOUVILLE TYPE THEOREMS OF SEMILINEAR EQUATIONS WITH SQUARE SUM OF VECTOR FIELDS

Let Xj,j=1,…k,be first order smooth quasi-homogeneous vector fields on R^n with the property that the dimension of the Lie algebra generated by these vector fields is n at x =0 and Xj^*--Xj,j=1,…,k,Let L=∑i=1^k Xi^2,In this paper,we study the nonnegative solutions of semilinear equation.     

BOUND STATES OF SCHRODINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS

We study the bound states to nonlinear Schr¨odinger equations with electromagnetic fields ih ?ψ/?t=(h/t▽-A(x))~2ψ + V(x)ψ-K(x)|ψ|~(p-1)ψ = 0, on R~+ × R~N. Let G(x) = [V(x)]~((p+1)/(p-1)-N/2) [K(x)](-(2/(p-1))) and suppose that G(x) has k local minimum points. For h 0 small, we find multi-bump bound states ψ_h(x, t) = e(-iE t/h)u_h(x) with uhconcentrating at the local minimum points of G(x) simultaneously as h → 0. The potentials V(x) and K(x)are allowed to be either compactly supported or unbounded at infinity.     

ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS

This paper considers the Calerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble （RFB） functions. The stability features of the residual-free bubble functions for the linearized Navier-Stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements.     

THE COMRENSATED COMPACTNESS METHOD APPLIED TO QUASILINEAR PARABOLIC EQUATIONS OF HIGHER ORDER WITH BOUBLY STRONG DEGENERATION

This paper applies the compensated compactnessmethod to the study of a class of quasilinear parbolic equations of higher order with doubly strong degeneration. Some existence and uniqueness results are proved under certain conditions.     

EXISTENCE OF SOLUTION FOR MODIFIED LANDAU-LIFSHITZ MODEL

In the present paper, the existence of solutions to Cauchy problem for modified Landau-Lifshitz Model initiated by Augusto Visintin is studied.     

MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

1. IntroductionWe deal with the Duffing equationi g(x) ~ p(t), (1.1)where g(x), p(t) E C(R, R) and p(t) is periodic, whose least period is 27. The multiplicityof periodic solutions of Equation (l.1) has been widely studied since the 50s. In [1], T.Ding studied the multiplicity of periodic solutions of Equation (1.1) under the followingconditions.(gi) Let g(x) E C'(R, R), and let K be a positive constant, such that(gi) There exist two constallts Ac > 0 and MO > 0 such thatg(x) w~ > AO…     

具有连续变量的差分方程的振动性

本文建立了具有连续交量差分方程的振动性判据，其结果改进了文献中的某些已知结果．     

具两个时滞项的微分方程的稳定性

本文考虑了一类具两个时滞项的微分方程的稳定性，其中一个时滞项的系数非负，另一个时滞项的系数非正．当非负系数恒为零时，本文所得结论改进了Yorke等提出的3/2稳定性定理的相应结论，当非负系数项的时滞为零，本文不同于已有文献用Liapunov函数或泛函法将时滞项作为干扰处理，而是反过来利用时滞项让方程稳定．     

具变时滞差分方程解的振动性

本文研究了一类具变时滞的非线性差分方程解的振动性,获得了该方程解的振动准则．将结论应用于差分方程ΔＸｎ ＋ ｐｎｘｎ－ ｋｎ ＝ ０　　ｎ ＝ ０,１,２,… （）其中ｐｎ≥０,｛ｋｎ｝是正整数数列且ｌｉｍｎ→∞｛ｎ－ ｋｎ｝＝ ∞．我们得到了方程（）振动的新的充分条件．     

具有连续变量的差分方程的振动性

本文建立了具有连续变量的差分方程ｙ（ｔ）－ｐ（ｔ）ｙ（ｔ－τ）＋ｑ（ｔ）ｙ（ｔ－σ）＝０的振动性判据，这里ｐ（ｔ），ｑ（ｔ）∈Ｃ［［０，∞），Ｒ＋］，τ＞０，σ＞０     

UNIQUENESS OF STATIONARY SOLUTIONS WITH VACUUM OF EULER-POISSON EQUATIONS

In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlineax transformation which is a functionof density and entropy the corresponding problem can be reduced to a semilinear ellipticequation with a nonlinear source term consisting of a power function, for which the classical     

有限元方法在一维和二维抛物方程参数辨识中的应用

§1.引言 本文考虑分布参数系统 ? 在Ω×[0,T]中的参数辨识问题,即通过u的某种观测确定参数a,f及u_0.但一般预先知道u_0和f,因而本文仅考虑参数a的辨识问题.(1)中的Ω是R~n中的有界区域,?Ω为其边界.     

变系数函数方程解的振动性

本文给出了变系数函数方程ｘ（ｇ（ｔ））＝Ｐ（ｔ）ｘ（ｔ）＋∑Ｑｉ（ｔ）ｘ（ｇｋ＋ｉ（ｔ））的一切解均ｉ＝１为振动的充分条件,其中Ｋ≥１为正整数．     

具有振动系数时滞差分方程解的振动性

本文研究了一类具振动系数时滞差分方程解的振动性,给出了一个新的振动准则,改进了已有文献中许多相关的结果．     

OSCILLATION OF ADVANCED DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS

The oscillations of the advanced difference equationsxn - xn-1 - p(n)xn+k = 0, n ≥ 0, (*)andXn - Xn-1 - ∑i=1mpi(n)xn+ki=0, n ≥0, (**)are investigated, where p(n),pi(n)(i = 1,2,..., m) are nonnegative real numbers. First. a sufficienet condition for the oscillation of equation (*) is obtained, then the result is generalized to the equation (**). At last, an example is given to illustrate the advantages of our results. Our results are new.     

GLOBAL LINEARIZATION OF DIFFERENTIAL EQUATIONS WITH SPECIAL STRUCTURES

This paper introduces the global linearization of the differential equations with special structures.The function in the differential equation is unbounded.We prove that the differential equation with unbounded function can be topologically linearlized if it has a special structure.     

DECAYING SOLUTIONS OF DIFFERENCEEQUATIONS WITH CONTINUOUS ARGUMENTS

1IntroductionItiswellknownthatdifferenceequationisanimportantmathematicaltoolinthestudyofscienceandtechnology11,2].Recently,theoscillationandstabilityofdifferenceequationsdefinedonasubsetofintegershavebeenextensivelyinvestigatedbymanyauthors,seeforexample…     

STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper,we obtain suffcient conditions for the stability in p-th moment of the analytical solutions and the mean square stability of a stochastic differential equation with unbounded delay proposed in [6,10] using the explicit Euler method.